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RADIATION, LIGHT AND
ILLUMINATION
A SERIES OF ENGINEERING LECTURES
DELIVERED AT UNION COLLEGE
BY
CHARLES PROTEUS STEINMETZ, A.M., PH.D.
>\
COMPILED AND EDITED BY
JOSEPH LEKOY HAYDEN
NEW YORK
McGRAW-HILL BOOK COMPANY
239 WEST 39TH STREET
1909
\ \
COPYRIGHT, 1909,
BT THE
McGRAW-HILL BOOK COMPANY
NEW YORK
AUTHOR'S PREFACE.
THE following lectures were given as a course of instruction to
the senior students in electrical engineering at Union University.
They are however intended not merely as a text-book of
illuminating engineering, nor as a text-book on the physics of
light and radiation, but rather as an exposition, to some extent,
from the engineering point of view, of that knowledge of light
and radiation which every educated man should possess, the
engineer as well as the physician or the user of light. For this
purpose they are given in such form as to require no special
knowledge of mathematics or of engineering, but mathematical
formalism has been avoided and the phenomena have been de-
scribed in plain language, with the exception of Lectures X and
XI, which by their nature are somewhat mathematical, and are
intended more particularly for the illuminating engineer, but
which the general reader may safely omit or merely peruse the
text.
The lectures have been revised to date before publication, and
the important results of the work of the National Bureau of
Standards, contained in its recent bulletins, fully utilized.
CHARLES PROTEUS STEINMETZ.
SCHENECTADY, September, 1909.
iii
COMPILER'S PREFACE.
A SERIES of eight experimental lectures on " Light and Radia-
tion" were delivered by Dr. Steinmetz in the winter of 1907-8
before the Brooklyn Polytechnic Institute. Unfortunately no
stenographer was present and no manuscript prepared by the
lecturer. A far more extended course of experimental lectures
was however given by Dr. Steinmetz at Union University in the
winter of 1908-9, on " Radiation, Light, Illumination and Illu-
minating Engineering," and has been compiled and edited in
the following.
Two additional lectures have been added thereto by Dr. Stein-
metz to make the treatment of the subject complete even from
the theoretical side of illuminating engineering : Lecture X on
"Light Flux and Distribution" and Lecture XI on "Light
Intensity and Illumination." These two lectures give the
elements of the mathematical theory of illuminating engineering.
With the exception of the latter two lectures the following
book contains practically no mathematics, but discusses the
subjects in plain and generally understood language.
The subject matter of Lecture XII on "Illumination and
Illuminating Engineering" has been given in a paper before the
Illuminating Engineering Society; the other lectures are new
in their form and, as I believe, to a considerable extent also in
their contents.
In describing the experiments, numerical and dimensional
data on the apparatus have been given, and the illustrations
drawn to scale, as far as possible, so as to make the repetition
of the experiments convenient for the reader or lecturer.
Great thanks are due to the technical staff of the McGraw-Hill
Book Company, which has spared no effort to produce the book
in as perfect a manner as possible.
JOSEPH L. R. HAYDEN.
SCHENECTADY, September, 1909.
CONTENTS.
LECTURE I. NATURE AND DIFFERENT FORMS OF RADIATION.
1. Radiation as energy. j
2. Measurement of the velocity of light. 2
3. Nature of light. 4
4. Difference of wave length with differences of color. Meas-
urement of wave length and of frequency. Iridescence.
The ether. 6
5. Polarization proving light a transversal vibration. Double
refraction. 7
6. The visible octave of radiation. Ultra-red and ultra-violet
radiation. 9
7. The electric waves. 15
8. The spectrum of radiation covering 60 octaves. 16
LECTURE II. RELATION OF BODIES TO RADIATION.
9. Electric waves of single frequency, light waves of mixed
frequency. 20
10. Resolving mixed waves into spectrum. Refraction. 21
11. Relation of refractive index to permeability and dielectric
constant. 24
12. Spectrum. 25
13. Continuous spectrum. Line spectrum. Band spectrum.
Combination spectra. 26
14. Reflection, absorption and transmission. 29
15. Conversion of absorbed radiation into heat and light. 30
16. Transmitted light. 31
17. Opaque colors and transparent colors. 32
18. Objective color and subjective color. 33
19. Effect of excess and of deficiency of certain wave length
of the illuminant on the opaque and the transparent
colors.
vii
viii CONTENTS.
PAGE
LECTURE III. PHYSIOLOGICAL EFFECTS OF RADIATION.
Visibility.
20. The eye. 37
21. Dependence of sensitivity of the eye on the color. Mechan-
ical equivalent of light. Comparison of intensities of
different colors. 40
22. Sensitivity curves of eye for different intensities. 43
23. Change of shape of sensitivity curve with intensity. 45
24. Harmful effect of excessive radiation power. 48
25. Protective action of eye. 50
26. Specific high frequency effect beginning in blue. 51
27. Perception of ultra-violet light. Harmful effects of ultra-
violet. 52
28. Arcs as producers of ultra-violet rays. 55
Pathological and Therapeutic Effects of Radiation.
29. Power effect and specific high frequency effect. 57
30. Light as germicide and disinfectant. 59
LECTURE IV. CHEMICAL AND PHYSICAL EFFECTS OF RADIATION.
Chemical Effects.
31. Indirect chemical action by energy of radiation. Direct
chemical action. 63
32. Chemical action of red and yellow rays in supplying the
energy of plant life. Destructive action of high frequency
on plant life. 64
Physical Effects.
33. Fluorescence and phosphorescence. 66
LECTURE V. TEMPERATURE RADIATION.
34. Production of radiation by heat. 70
35. Increase of intensity and frequency with temperature. 73
36. Efficiency and temperature. 76
37. Carbon incandescent lamp. 78
38. Evaporation below boiling point. Allotropic modifications
of carbon. 81
39. Normal temperature radiation. 84
40. Colored body radiation. 85
41. Measurement of temperatures by radiation. 89
42. Colored radiation and heat luminescence. 90
CONTENTS. ix
PAGE
LECTURE VI. LUMINESCENCE.
Fluorescence and Phorphorescence.
43. Radioluminescence. Electroluminescence. Thermolumi-
nescence. Physical phosphorescence. Chemical phos-
phorescence. Biological phosphorescence. 94
44. Pyroluminescence. Chemical luminescence. 96
45. Electroluminescence of gases and vapors. 98
Disruptive Conduction.
46. Geissler tube and spark. Disruptive voltage. 101
47. Change from spark to Geissler glow. 105
Continuous Conduction.
48. Nature of continuous or arc conduction. 106
49. Distinction between arc and spark discharge. Ill
50. Continuity at negative. 113
51. Rectification of alternating voltages by arcs. 117
52. Efficiency and color. 122
53. Most efficient light producer. 123
54. Electro-conduction from negative, long life, non-consuming
positive, limitation in the available materials. 125
55. Arc most efficient method of light production. 126
LECTURE VII. FLAMES AS ILLUMINANTS.
56. Hydrocarbon flames. 128
57. Effect of rapidity of combustion and of flame shape on
smokiness. 130
58. Effect of oxygen atom in the hydrocarbon molecule on
luminosity. 132
59. Mixture of hydrocarbon with air. 133
60. Chemical luminescence. 134
61. Flames with separate radiator. 135
LECTURE VIII. ARC LAMPS AND ARC LIGHTING.
Volt- Ampere Characteristics of the Arc.
62. Arc length and voltage. 137
63. General equations of the arc. 140
Stability Curves of the Arc.
64. Instability on constant voltage.. 142
65. Equations of the vapor arc. 145
Arc Length and Efficiency.
66. Maximum efficiency length of carbon arc. 146
67. Maximum efficiency length of luminous arc. 148
X CONTENTS.
PAGE
LECTURE VIII. ARC LAMPS AND ARC LIGHTING (Continued).
Arc Lamps.
68. The elements of the arc lamp. 151
69. Differential arc lamp. 153
70. Series arc lamp. 157
71. Luminous arc lamp. 160
Arc Circuits.
72. Constant potential and constant current. The mercury
arc rectifier system. The arc machine. 160
73. The constant current transformer. The constant current
reactance. 163
LECTURE IX. MEASUREMENT OF LIGHT AND RADIATION.
74. Measurement of radiation as power. 166
75. Light a physiological quantity. 167
76. Physiological feature involved in all photometric methods. 169
77. Zero method photometers. 170
78. Comparison of lights. 172
79. Flicker photometer. 173
80. The luminometer. 175
81. Primary standards of light. 177
82. Proposed primary standards. 178
83. Illumination and total flux of light. Incandescent lamp
photometry. 179
84. Arc lamp photometry. 182
85. Discussion. Mean spherical, horizontal, downwards, maxi-
mum, hemispherical candle power. 184
LECTURE X. LIGHT FLUX AND DISTRIBUTION.
86. Light flux, light flux density, light intensity. 186
87. Symmetrical and approximately symmetrical distribution. 187
88. Calculation of light flux from meridian curve of symmetri-
cal radiator. 188
Distribution Curves of Radiation.
89. Calculation of distribution curves. Point or sphere of
uniform brilliancy. 190
90. Straight line or cylindrical radiator. 195
91. Circular line or cylinder. 197
92. Single loop filament incandescent lamp as illustration. 200
CONTENTS. xi
PAGE
LECTURE X. LIGHT FLUX AND DISTRIBUTION (Continued).
Shadows.
93. Circular shade opposite and symmetrical to circular radia-
tor. 202
94. Calculation of the meridian curves of a circular radiator, for
different sizes of a symmetrical circular shade, and for
different distances of it. 206
95. Circular shade concentric with end of linear radiator. 210
Reflection.
96. Irregular reflection. 212
97. Regular reflection. 215
98. Reflector with regular and irregular reflection. 218
Diffraction, Diffusion and Refraction.
99. Purpose of reducing the brilliancy of the illuminant. 221
100. Effect of the shape of the diffusing globe on the distribu-
tion curve. 223
101. Prismatic refraction and reflection. 224
LECTURE XI. LIGHT INTENSITY AND ILLUMINATION.
Intensity Curves for Uniform Illumination.
102. Calculation of intensity distribution of illuminant for
uniform total, horizontal and vertical illumination. 226
103. Uniform illumination of limited area. 229
Street Illumination by Arcs.
104. Discussion of problem. 234
105. Combined effect of successive lamps.
Room Illumination by Incandescent Lamps.
106. Distribution curve of lamp. Calculation of resultant total
intensity of direct light.
107. Reflection from walls and ceiling. 246
108. Total directed and diffused illumination. 251
Horizontal Table Illumination by Incandescent Lamps.
109. Location of lamps. 253
xii CONTENTS.
PAGE
LECTURE XII. ILLUMINATION AND ILLUMINATING ENGINEERING.
110. Physical and physiological considerations. 256
111. Light flux density. Illumination. Brilliancy. 259
112. Physical problems. Ceilings and walls. Reflectors, diffus-
ing globes, diffracting shades, etc. 260
113. Objective illumination. Subjective illumination. Con-
traction of pupil. Intrinsic brilliancy. Direct and in-
direct lighting. 261
114. Fatigue. 263
115. Differences in intensity and in color. Control of color
differences. Shadows and their control. Directed and
diffused light. 265
116. Direction of shadows. 267
117. Color sensitivity in relation to required intensity of illu-
mination. 269
118. Domestic lighting. 270
119. The twofold problem of domestic lighting: daylight and
artificial light. 271
120. Street lighting. 272
121. Defects of present street lighting. 273
122. Tower lighting. 274
LECTURE XIII. — PHYSIOLOGICAL PROBLEMS OF ILLUMINATING
ENGINEERING.
123. Physical side of illuminating engineering. Physiological
problems. 277
124. Physiological difference between diffused and directed
light. 278
125. Indefmiteness of diffused light. Shadows cast by diffused
daylight. Equivalent diffusion near light source of
large extent. 279
126. Equivalent diffusion by using several light sources. 281
127. Unequal diffusion in different directions. Complex
shadows. 282
128. Physiological light distribution. 283
129. Physiologically, light not a vector quantity. 284
130. Resultant effect of several light sources. 287
RADIATION, LIGHT, AND
ILLUMINATION.
LECTURE I.
NATURE AND DIFFERENT FORMS OF RADIATION.
1. Radiation is a form of energy, and, as such, can be produced
from other forms of energy and converted into other forms of
energy.
The most convenient form of energy for the production of rad-
iation is heat energy, and radiation when destroyed by being
intercepted by an opaque body, usuaDy is converted into heat.
Thus in an incandescent lamp, the heat energy produced by the
electric current in the resistance of the filament, is converted
into radiation. If I hold my hand near the lamp, the radiation
intercepted by the hand is destroyed, that is, converted into heat,
and is felt as such. On the way from the lamp to the hand, how-
ever, the energy is not heat but radiation, and a body which is
transparent to the radiation may be interposed between the
lamp and the hand and remains perfectly cold. The terms
"heat radiation " and " radiant heat," which are occasionally
used, therefore are wrong: the so-called radiant heat is not heat
but radiation energy, and becomes heat only when, intercepted
by an opaque body, it ceases to be radiation; the same, however,
applies to any radiation. If we do not feel the radiation of a
mercury lamp or that of the moon as heat, while we feel that of a
coal fire, it is merely because the total energy of the latter is very
much greater; a sufficiently sensitive heat-measuring instrument,
as a bolometer, shows the heat produced by the interception of
the rays of the mercury lamp or the rays of the moon.
The most conspicuous form of radiation is light, and, therefore,
it was in connection with this form that the laws of radiation
were first studied.
1
2 RADIATION, LIGHT, AND ILLUMINATION.
2. The first calculations of the velocity of light were made by
astronomers in the middle of the eighteenth century, from the
observations of the eclipses of the moons of Jupiter. A number
of moons revolve around the planet Jupiter, some of them so close
that seen from the earth they pass behind Jupiter and so are
eclipsed at every revolution. As the orbits of Jupiter's moons
were calculated from their observations by the law of gravita-
tion, the time at which the moon M should disappear from sight,
FIG. 1.
when seen from the earth E, by passing behind Jupiter, 7 (Fig. 1),
could be exactly calculated. It was found, however, that some-
times the moon disappeared earlier, sometimes later than cal-
culated, and the difference between earliest and latest disappear-
ance amounts to about 17 min. It was also found that the
disappearance of the moon behind Jupiter occurred earlier when
the earth was at the same side of the sun as Jupiter, at A, while
the latest disappearance occurred when the earth was on the
opposite side of the sun from Jupiter, at B. Now, in the latter
case, the earth is further distant from Jupiter by the diameter
ASB of the orbit of the earth around the sun S, or by about
195,000,000 miles and the delay of 17J min. thus must be due to
the time taken by the light to traverse the additional distance
of 195,000,000 miles. Seventeen and one-third min. are 1040
sec. and 195,000,000 miles in 1040 sec. thus gives a velocity of
light of » or 188,000 miles per sec.
Later, the velocity of light was measured directly in a number
of different ways. For instance, let, in Fig. 2, D be a disk per-
forated with holes at its periphery. A lamp L sends its light
through a hole H0 in the disk to a mirror M located at a con-
siderable distance, for instance 5 miles; there the light is reflected
NATURE AND DIFFERENT FORMS OF RADIATION. 3
and the mirror is adjusted so that the reflected beam of light
passes through another hole Hl of the disk into the telescope T.
If the disk is turned half the pitch of the holes the light is blotted
out as a tooth stands in front of both the lamp and the telescope.
Again turning the disk half the pitch of the holes in the same
5_MOE_S
FIG. 2.
direction the light reappears. If the disk is slowly revolved, alter-
nate light and darkness will be observed, but when the speed in-
creases so that more than from 10 to 20 holes pass per second, the
eye is no longer able to distinguish the individual flashes of light
but sees a steady and uniform light; then increasing the speed
still more the light grows fainter and finally entirely disappears.
This means when a hole H0 is in front of the lamp, a beam of
light passes through the hole. During the time taken by the light
to travel the 10 miles to the mirror and back, the disk D has
moved, and the hole Hv which was in front of the telescope
when the light from the lamp passed through the hole HQ, has
moved away, and a tooth is now in front of the telescope and
intercepts the light. Therefore, at the speed at which the light
disappears, the time it takes the disk to move half the pitch of a
hole is equal to the time it takes the light to travel 10 miles.
Increasing still further the velocity of the disk D, the light
appears again, and increases in brilliancy, reaching a maximum
at twice the speed at which it had disappeared. Then the light
reflected from the mirror M again passes through the center of
a hole into the telescope, but not through the same hole Ht
through which it would have passed with the disk stationary, but
through the next hole H2, that is, the disk has moved a distance
equal to the pitch of one hole while the light traveled 10 miles.
Assume, for instance, that the disk D has 200 holes and makes
4 RADIATION, LIGHT, AND ILLUMINATION.
94 rev. per sec. at the moment when the light has again reached
full brilliancy* In this case, 200 X 94 = 18,800 holes pass the
telescope per second, and the time of motion by the pitch of one
hole is sec., and as this is the time required by the light
18,800
to travel 10 miles, this gives the velocity of light as 10 •* >
lo,oOU
or 188,000 miles per sec.
The velocity of light in air, or rather in empty space, thus is
188,000 miles or 3 X 1010 cm. per sec.
For electrical radiation, the velocity has been measured by
Herz, and found to be the same as the velocity of light, and there
is very good evidence that all radiations travel with the same
velocity through space (except perhaps the rays of radioactive
substances).
3. Regarding the nature of radiation, two theories have been
proposed. Newton suggested that light rays consisted of
extremely minute material particles thrown off by the light-
giving bodies with enormous velocities, that is, a kind of bom-
bardment. This theory has been revived in recent years to
explain the radiations of radium, etc. Euler explained the light
as a wave motion. Which of these explanations is correct
can be experimentally decided in the following manner: Assum-
ing light to be a bombardment of minute particles, if we com-
bine two rays of light in the same path they must add to each
other, that is, two equal beams of light together give a beam of
twice the intensity. If, however, we assume light is a wave
motion, then two equal beams of light add to one of twice the
intensity only in case the waves are in phase, as Al and B^ in
Fig. 3 add to Cr If, however, the two beams A2 and B2 are not
in phase, their resultant C2 is less than their sum, and if the
two beams A3 and B3 in Fig. 3 happen to be in opposition
(180 degrees apart), that is, one-half wave length out of phase
with each other, their resultant is zero, that is, they blot each
other out.
Assuming now we take a plain glass plate A (Fig. 4) and a
slightly curved plate B, touching each other at (7, and illuminate
them by a beam of uniform light — as the yellow light given by
coloring the flame of a bunsen burner with some sodium salt —
a part of the light b, is then reflected from the lower surface of
NATURE AND DIFFERENT FORMS OF RADIATION. 5
the curved glass plate B, a part c, passes out of it, and is reflected
from the upper surface of the plain glass plate A. A beam of
FIG. 3.
reflected light a, thus is a combination of a beam b and a beam c.
The two beams of light which combine to a single one, a, differ
from each other in phase by twice the distance between the two
glass plates. At those points dv dv etc. at which the distance
FIG. 4.
between the two glass plates is J wave length, or j, J, etc., the
two component beams of a would differ by \, f , |, etc. wave
lengths, and thus would blot each other out, producing darkness,
6 RADIATION, LIGHT, AND ILLUMINATION.
while at those points where the distance between the glass plates
is J, 1, lj, etc. wave lengths, and the two component beams a
thus differ in phase by a full wave or a multiple thereof, they
would add. If, therefore, light is a wave motion, such a structure
would show the contact point C of the plates surrounded by
alternate dark rings, d, and bright rings, y. This is actually the
case, and therefore this phenomenon, called " interference"
proves light to be a wave motion, and has lead to the universal
acceptance of the Eulerian theory.
Measuring the curvature of the plate B, and the diameter
of the dark rings d, the distance between the plates B and A at
the dark rings d, can be calculated and as this distance is one-
quarter wave length, or an odd multiple thereof, the wave
length can be determined therefrom.
The wave length of light can be measured with extremely high
accuracy and has been proposed as the absolute standard of
length, instead of the meter, which was intended to be 10~7 of
the quadrant of the earth.
4. It is found, however, that the different colors of light have
different wave lengths; red light has the greatest wave length,
and then in the following order: red, orange, yellow, green, blue,
indigo, violet, the wave length decreases, violet light having the
shortest wave length.
If in experiment (Fig. 4) instead of uniform light (monochro-
matic light), ordinary white light is used, which is a mixture of
all colors, the dark and bright rings of the different colors appear
at different distances from each other, those of the violet near-
est and those of the red the furthest apart, and so superimpose
upon each other, and instead of alternately black and light rings,
colored rings appear, so-called interference rings. Wherever a
thin film of air or anything else of unequal thickness is inter-
posed between two other materials, such interference colors thus
appear. They show, for instance, between sheets of mica, etc.
The colors of soap bubbles are thus produced.
The production of such colors by the interference of rays of
light differing from each other by a fractional wave length is
called iridescence.
Iridescent colors, for instance, are those of mother-of-pearl,
of opal, of many butterflies, etc.
Light, therefore, is a wave motion.
NATURE AND DIFFERENT FORMS OF RADIATION. 1
The frequency of radiation follows from the velocity of light,
and the wave length.
The average wave length of visible radiation, or light, is about
lw = 60 microcentimeters,* that is, 60 X 10~8 cm. (or about
^<y^<5-<y in.) and since the speed is S = 3 X 1010 cm. the frequency
a
is / = r- = 500 X 1012, or 500 millions of millions of cycles per
LW
second, that is, inconceivably high compared with the frequencies
with which we are familiar in alternating currents.
If, as proven, light is a wave motion, there must be some thing
which is moving, a medium, 'and from the nature of the wave
motion, its extremely high velocity, follow the properties of this
medium: it has an extremely high elasticity and extremely low
density, and it must penetrate all substances since no vacuum can
be produced for this medium, because light passes through any
vacuum. Hence it cannot be any known gas, but must be essen-
tially different, and has been called the "ether."
Whether the ether is a form of matter or not depends upon
the definition of matter. If matter is defined as the (hypotheti-
cal) carrier of energy (and all the information we have of matter
is that it is the seat of energy) , then the ether is matter, as it is a
carrier of energy: the energy of radiation, during the time be-
tween the moment when the wave leaves the radiator and the
moment when it strikes a body and is absorbed, resides in the
ether.
5. If light is a wave motion or vibration, it may be a longitudi-
nal vibration, or a transversal vibration; that is, the particles of
the medium which transmit the vibrations may move in the
direction in which the wave travels, as is the case with sound
waves in air. If in Fig. 5 sound waves travel from the bell B in
the direction BA, the air molecules m vibrate in the same direction,
A to B. Or the vibration may be transversal ; that is, if the beam
* As measures of the wave length of light, a number of metric units have
survived and are liable to lead to confusion:
The micron, denoted by ft, equal to one thousandth of a millimeter.
The fJLfJ., equal to one millionth of a millimeter.
The Angstrom unit, equal to one ten-millionth of a millimeter.
As seen, the basis of these units is the millimeter, which was temporarily
used as a standard unit of length before the establishment of the present
absolute system of units, the (C.G.S), which is based on centimeter length,
gram mass, and second time measure.
A radiation of the wave length of 60 microcentimeters thus can be expressed
also as: 6000 Angstrom units, or 0.6 p, or 600 pp.
8 RADIATION, LIGHT, AND ILLUMINATION.
of light moves in Fig. 6 perpendicularly to the plane of the paper,
the vibrating particles move in any one of the directions oa, ob,
etc. in the plane of the paper, and thus perpendicular to the ray
FIG. 5.
of light. In the former case (a longitudinal vibration, as sound)
there obviously can be no difference between the directions at
right angles to the motion of the wave. In a transversal vibra-
tion, however, the particles may move either irregularly in any
of the infinite number of directions at right angles to the ray
(Fig. 6) and thus no difference exists in the different directions
perpendicular to the beam, or they may vibrate in one direction
only, as the direction boa (Fig. 7). In the latter case, the wave is
called " polarized" and has differ-
ent characteristics in three direc-
tions at right angles to each other :
one direction is the direction of
propagation, or of wave travel; the
second is the direction of vibration;
IG' 6' and the third is the direction per-
pendicular to progression and to vibration. For instance, the
electric field of a conductor carrying alternating current is a
polarized wave: the direction parallel to the conductor is the
direction of energy flow; the direction concentric to the con-
ductor is the direction of the electromagnetic component, and
the direction radial to the conductor is the direction of the
electrostatic component of the electric field.
Therefore, if light rays can be polarized, that is, made to ex-
hibit different properties in two directions at right angles to each
other and to the direction of wave travel, this would prove tke
light wave to be a transversal vibration. This is actually the case.
For instance, if a beam of light is reflected a number of times
under a fairly sharp angle, as shown in Fig. 8, this beam becomes
polarized ; that is, for instance, the reflection from the mirror m0,
set like the mirrors mv m2 . . . which produced the polarization,
NATURE AND DIFFERENT FORMS OF RADIATION. 9
is greater, and the absorption less than from a mirror set at right
angles thereto, as ra/.
Some crystals, as Iceland spar (calcium carbonate), show
"double refraction," that is, dissolve a beam of light, a, enter-
ing them into two separate beams, b and c (Fig. 9) which are
polarized at right angles to each other.
In a second crystal, K2, beam b would then enter as a single
beam, under the same angle as in the first crystal Kv if K2 were
in the same position as Kl ; while if K2 were turned at right angles
to Kv beam b would enter K2 under the same angle as beam c in
crystal Kr
6. As seen, light and radiation in general are transversal wave
motions of very high speed, S = 3 X 1010 cm. per sec. in a hypo-
thetical medium, ether, which must be assumed -to fill all space
and penetrate all substances.
Radiation is visible, as light, in a narrow range of frequencies
only: between 400 X 1012 and 770 X 1012 cycles per sec. cor-
responding to wave lengths from 76 X 10"6 cm. to 39 X 10"' cm.*
All other radiations are invisible and thus have to be observed by
other means.
I have here a pair of rods of cast silicon (10 in. long, 0.22 in. in
diameter, having a resistance of about 10 ohms each), connected
* The visibility of radiation is greatest between the wave lengths 50 X 10~*
to 60 X 10~e and good between the wave lengths 41 X 10~e to 76 X 10~8,
but extends more or less indistinctly over the range of wave lengths from
33 X 10~6 to 77 X 10~6 and faintly even as far as 30 X 10~fl to 100 X
10
RADIATION, LIGHT, AND ILLUMINATION.
in series with each other and with a rheostat of about 40 ohms
resistance in a 120-volt circuit. When I establish a current
through the rods, electric energy is converted into heat by the
resistance of the rods. This heat energy is converted into and
sent out as radiation, with the exception of the part carried off
by heat conduction and convection. Reducing the resistance, I
increase the heat, and thereby the radiation from the silicon rods.
Still nothing is visible even in the dark; these radiations are of
too low frequency, or great wave length, to be visible. By hold-
ing my hand near the rods, I can feel the energy as heat, and show
it to you, by bringing the rods near to this Crookes' radiometer,
FIG. 9.
which is an instrument showing the energy of radiation. It con-
sists (Fig. 10) of four aluminum vanes, mounted in a moderately
high vacuum so that they can move very easily. One side of each
vane is polished, the other blackened. The waves of radiation
are reflected on the polished side of the vane; on the blackened
side they are absorbed, produce heat, thus raise the temperature of
the air near the vane; the air expands and pushes the vanes ahead,
that is, rotates the wheel. As you see, when I bring the heated
rods near the radiometer, the wheel spins around at a rapid rate
by the radiation from the rods, which to the eye are invisible.
NATURE AND DIFFERENT FORMS OF RADIATION. 11
Increasing still further the energy input into the silicon rods, and
thereby their temperature, the intensity of radiation increases,
'but at the same time radiations of higher and higher frequencies
appear, and ultimately the rods become visible in the dark,
giving a dark red light; that is, of all the radiations sent out by
the rods, a small part is of sufficiently high frequency to be visible.
Still further increasing the tempera-
ture, the total radiation increases,
but the waves of high frequency in-
crease more rapidly than those vof
lower frequency ; that is, the average
frequency of radiation increases or
the average wave length decreases
and higher and higher frequencies
appear, — orange rays, yellow, green,
blue, violet, and the color of the
light thus gradually changes to
bright red, orange, yellow. Now I
change over from the silicon rods —
which are near the maximum tem-
perature they can stand — to a tung-
sten lamp (a 40- watt 110- volt lamp,
connected in series with a rheostat
of 2000 ohms resistance in a 240-
volt circuit). For comparison I also
turn on an ordinary 16 c. p. carbon
filament incandescent lamp, running
at normal voltage and giving its
usual yellow light. Gradually turn-
ing out the resistance, the light of
the tungsten lamp changes from
orange to yellow, yellowish white
and ultimately, with all the resistance cut out and the fila-
ment running at more than double voltage, is practically white;
that is, gives a radiation containing all the frequencies of visible
light in nearly the same proportion as exist in sunlight. If we
should go still further and very greatly increase the temperature,
probably because of the more rapid increase of the higher fre-
quencies (violet, blue, green) than the lower frequencies of light
(red, orange and yellow) with increase in temperature, the light
FIG. 10.
12
RADIATION, LIGHT, AND ILLUMINATION.
would become bluish. However, we are close to the limit of
temperature which even tungsten can stand, and to show you
light of high frequency or short wave length I use a different
apparatus in which a more direct conversion of electric energy
into radiation takes place, — the mercury arc lamp. Here the
light is bluish green, containing only the highest frequencies
of visible radiation, violet, blue and green, but practically none
of the lower frequencies of visible radiation, red or orange.
FIG. 11.
In the tungsten lamp at high brilliancy and more still in the
mercury arc, radiations of higher frequencies appear, that is,
shorter wave lengths than visible light, and these radiations are
again invisible. As they are of frequencies beyond the violet
rays of light, they are called " ultra-violet rays/' while the radia-
tions which we produced from the heated silicon rods at moderate
temperatures were invisible because of too low frequency and
are thus called " ultra-red rays," or " infra-red rays/' as they are
outside of and below the red end of the range of visible radiation.
To produce powerful ultra-violet rays, I use a condenser dis-
charge between iron terminals, a so-called ultra-violet arc lamp.
Three iron spheres, 7 in Fig. 11, of about f in. diameter, are
mounted on an insulator B. The middle sphere is fixed, the
NATURE AND DIFFERENT FORMS OF RADIATION. 13
outer ones adjustable and set for about ^ in. gap. This lamp is
connected across a high voltage 0.2-mf. mica condenser C, which
is connected to the high voltage terminal of a small step-up trans-
former T giving about 15,000 volts (200 watts, 110 •*- 13,200
volts). The low tension side of the transformer is connected to
the 240-volt 60-cycle circuit through a rheostat R to limit the
current. The transformer charges the condenser, and when the
voltage of the condenser has risen sufficiently high it discharges
through the spark gaps I by an oscillation of high frequency
(about 500,000 cycles), then charges again from the transformer,
discharges through the gap, etc. As several such condenser dis-
charges occur during each half wave of alternating supply voltage
the light given by the discharge appears continuous.
You see, however, that this iron arc gives apparently very little
light; most of the radiation is ultra-violet, that is, invisible to the
eye. To make it visible, we use what may be called a frequency
converter of radiation. I have here a lump of willemite (native
zinc silicate), a dull greenish gray looking stone. I put it under
the iron arc and it flashes up in a bright green glare by convert-
ing the higher frequency of ultra-violet rays into the lower
frequency of green light. This green light is not given by the
iron arc, as a piece of white paper held under the arc shows only
the faint illumination given by the small amount of visible radia-
tion. I now move a thin sheet of glass, or of mica, between the
iron arc and the lump of willemite, and you see the green light
disappear as far as the glass casts a shadow. Thus glass or mica,
while transparent to visible light, is opaque for the ultra-violet
light of the iron arc. A thick piece of crystallized gypsum (sel-
enite) put in the path of the ultra-violet light does not stop it,
hence is transparent, as the lump of willemite continues to show
the green light, or a piece of cast glass its blue light.
I have here some pieces of willemite in a glass test tube. They
appear dull and colorless in the ultra-violet light, as the glass is
opaque for this light. I shift them over into a test tube of fused
quartz, and you see them shine in the green glare. Quartz is trans-
parent to ultra-violet light. When investigating ultra-violet
light, quartz lenses and prisms must, therefore, be used.
Still higher frequencies of ultra-violet light than those given
by a condenser discharge between iron terminals are produced by
a low temperature mercury arc. Obviously this arc must not be
14 RADIATION, LIGHT, AND ILLUMINATION.
operated in a glass tube but in a quartz tube, as glass is opaque
for these rays.
These ultra-violet radiations carry us up to frequencies of about
3000 X 1012 cycles per sec., or to wave lengths of about 10 X 10~6
cm. Then, however, follows a wide gap, between the highest
frequencies of ultra-violet radiation and the frequencies of X-rays.
In this gap, radiations of very interesting properties may some-
times be found.
At the extreme end of the scale we find the X-rays and the
radiations of radio-active substances — if indeed these radiations
are wave motions, which has been questioned. Since at these
extremely high frequencies reflection and refraction cease, but
irregular dispersion occurs, the usual methods of measuring wave
lengths and frequencies fail. The X-rays apparently cover quite
a range of frequency and their average wave length has been
estimated as 0.01 X 10~6 cm., giving a frequency of 3 X 1018
cycles per sec.
In comparing vibrations of greatly differing frequencies, the
most convenient measure is the octave, that is, the frequency scale
of acoustics. One octave represents a doubling of the frequency ;
n octaves higher then means a frequency 2n times as high, n
octaves lower, a frequency Jn as high. By this scale all the inter-
vals are of the same character; one octave means the same
relative increase, which ever may be the absolute frequency or
wave length.
As the perceptions of our senses vary in proportion to the per-
centual change of the physical quantity causing the perception
(Fechner's law), in the acoustic or logarithmic scale the steps are
thus proportional to the change of sensual perception caused by
them.
The visible radiation covers somewhat less than one octave;
ultra-violet radiations have been observed beyond this for about
two more octaves. Ten octaves higher is the estimated frequency
of X-rays.
On the other side of the visible range, towards lower frequencies
or longer waves, ultra-red rays, observations have been extended
over more than eight octaves up to wave lengths as great as 0.03
cm. length, or frequencies of only 10 12 cycles per sec. The ultra-
red rays given by the heated silicon rods of our experiment do not
extend to such low frequencies, but such very low frequencies
NATURE AND DIFFERENT FORMS OF RADIATION. 15
have been observed in the radiations of bodies of very low tem-
perature, as liquid air, or in the moon's rays.
7. Very much longer waves, however, are the electric waves.
They are used in wireless telegraphy, etc. I here connect (Fig. 12)
FIG. 12.
the condenser C of the apparatus which I used for operating the
ultra-violet arc, to a spark gap Gv of which the one side is con-
nected to ground Bv the other side to a vertical aluminum rod Alf
about 8 feet long. The charge and discharge of the aluminum
rod Al by the oscillating condenser current, send out an electric
wave of about 50 feet length. This wave passes through you, and
when striking the aluminum rod A2 back of you, induces therein
an electric charge. A2 is separated from ground B2 by a narrow
spark gap G2 between graphite terminals, and the arrival of the
electric wave at A2 causes a small spark to jump across the gap
Gv which closes the circuit of the tungsten lamp L, thereby
lighting it as long as the wave train continues.
16 RADIATION, LIGHT, AND ILLUMINATION.
The electric waves used in wireless telegraphy range in wave
lengths from 100 feet or less to 10,000 feet or more, corresponding
to 107 to 105 cycles per sec.
Still very much longer waves are the fields of alternating cur-
rent circuits: the magnetic and electrostatic field of an alterna-
ting current progresses as a wave of radiation from the conductor.
But as the wave length is very great, due to the low frequency, —
3 X 1010
a 60-cycle alternating current gives a wave length of ^ =
500 X 10" cm. or 3100 miles — the distance to which the field of
the circuit extends is an insignificant fraction only of the wave
length, and the wave propagation of the field thus is usually not
considered.
Electric waves of higher frequencies than used in wireless
telegraphy are the Herzian waves, produced by electric oscilla-
tors, that is, a moderately long straight conductor cut in the
middle by a gap and terminated by spherical condensers, as
shown in Fig. 13. On these waves the velocity of propagation
< EN ERGY-SU PPLY-
o — ^^ — o
FIG. 13.
has been measured by Herz by producing standing waves by
combination of main wave and reflected wave.
Still much higher frequencies are the oscillations between the
cylinders of multi-gap lightning arresters, and the limit of fre-
quency of electric waves would probably be given by the oscilla-
ting discharge of two small spheres against each other when
separated by a narrow gap. It probably is at about 5 X 1010
cycles, or 0.6 cm. wave length.
The blank space between the longest electric wave and the
shortest ultra-violet light wave thus has become fairly narrow:
from 0.6 to 0.03 cm., or only about four octaves.
8. In the following tables, the different known forms of radia-
tion are arranged by their frequency and wave length, and also
given in octaves, choosing as zero1 point the middle c of the piano,
or a frequency of 128 cycles per sec.
UNIVERSITY
OF
NAT
IFFERENT FORMS OF RADIATION. 17
SPECTRUM OF RADIATION.
Zero point chosen at c = 128 cycles per second.
Speed of radiation S = 3 X lu10 cm.
Cycles.
Wave Length in Air
(or Vacuum).
Octave: Q^/
£.
Alternating current
1>
field:
15
20,000 km. = 12,500 mi.
25
12.000 km. = 7, 500 mi.
3.15
60
5, 000 km. = 3, 100 mi.
133
2,250 km. = 1,400 mi.
High frequency cur- \
rents, surges and
oscillations, arcing V
(9.57)
31.64
grounds, lightning
phenomena, etc. J
Wireless telegraph (
105
3 km. = 10,000 ft.
9.63 ) A ~,
waves : (
107
30 m. = 100 ft.
16.25 \ 6'62
Herzian waves:
107
109
30 m. = 100 ft.
30 cm. = 1 ft.
16.25 )
22.90 I 12.3
Limit of electric waves :
6X1010
0.6 cm. = 0.25 in.
28.55 ) )
First gap :
[4.25]
Ultra-red rays :
10'2
4X10'
30,000x10-" =0.03 cm.
76xlO~8 cm.
3280 ) ftAQ
41.48 f b>ba
Visible light rays : j
7.7X10'
76xlO-6cm.
39xlO~e cm.
41.48 i ft Q7
42.45 ] U<y/
11.6
Ultra-violet rays :
7.7X10'
30X101
39X10-6 cm.
10 x 10"8 cm.
42.45 ) , Q.
44.40 f 1'wo
Second gap:
[8.0]
X-rays (estimated) :
3X10'8
0.01 xlO~J cm.
54.4
Sound Waves :
Total :
57.7 octaves
Lowest audible sound :
15
66 ft. in air
-3.1
Highest audible sound :
8000
1.5 in. in air
+ 6.0
Total :
9.1 octaves
These radiations are plotted graphically in Fig. 14, with the
octave as abscissae.
As seen, the total range of frequencies of radiation is enormous,
covering nearly 60 octaves, while the range of sound waves is
only about nine octaves, from 15 to 8000 cycles.
There are two blank spaces in the range of radiation, one be-
tween electric and light waves, and a second and longer one
between light and X-rays.
It is interesting to note that the range of electric waves is far
greater than that of light waves.
Only a very narrow range of radiation, less than one octave out
of a total of 60, is visible. It is shown shaded in Fig. 14. This
18
RADIATION, LIGHT, AND ILLUMINATION.
exhibits the great difficulty of the problem of efficient light pro-
duction : it means producing as large a part of the total radiation
as possible within this very narrow range of visibility.
Regarding the range of frequencies covered by it, the eye thus is
much less sensitive than the ear, which hears over eight octaves
as sound waves.
While the visible radiations are the most important ones, as
light, the total range of radiation is of interest to the electrical
engineer.
The ultra-red rays are those radiations which we try to avoid
as far as possible when producing light, as they consume power
FIG. 14.
and so lower the efficiency; the ultra-violet rays are of importance
in medicine as germ killers. They are more or less destructive
to life, appear together with the visible radiation, and where they
are of appreciable amount, as in the arc, protection against them
becomes desirable. The X-rays have become of importance in
medicine, etc., as they penetrate otherwise opaque bodies and thus
allow seeing things inside of other bodies.
The total range of electric waves, between the frequencies of
alternating currents and the limits of electric waves, has been of
importance to the electrical engineer as harmful and destructive
phenomena in electric circuits, which are to be guarded against,
and only in recent years, with the development of wireless
telegraphy, some such electric waves have found a useful com-
mercial application. The main object of their study — which is
the study of transient electric phenomena, is still, however, to
guard against their appearance in electric circuits and discharge
them harmlessly when they appear.
Considering the great difference which already exists between
alternating currents of low frequency, 25 or 15 cycles, and of high
NATURE AND DIFFERENT FORMS OF RADIATION. 19
frequency, 133 cycles, and realizing that the total range of waves,
which may appear in electric circuits is many times greater than
the difference between high and low frequency alternating cur-
rents, it can be realized that the differences in the character of
electric waves are enormous between the low frequency surges of
near machine frequency and the high frequency oscillations of a
multi-gap lightning arrester, near the upper limits of electric wave
frequencies, and the problem of protecting circuits against them
thus is vastly more difficult than appears at first sight and the
conclusions drawn from experimental investigations of electric
waves may be very misleading when applied to waves many
octaves different from those used in the experiment. This ex-
plains the apparently contradictory evidence of many experi-
mental investigations on the protection of electric circuits.
LECTURE II.
RELATION OF BODIES TO RADIATION.
9. For convenience, the total range of known radiations can
be divided into two classes, the electric waves and the light waves,
which are separated from each other by the blank space in the
middle of the spectrum of radiation (Fig. 14). Under light
waves we here include also the invisible ultra-red radiation and
the ultra-violet radiation and the non-refrangible radiations, as
X-rays, etc., separated from the latter by the second blank
space of the radiation spectrum.
In the following, mainly the light waves, that is, the second or
high frequency range of radiation, will be discussed. The elec-
tric waves are usually of importance only in their relation to the
radiator or oscillator which produces them, or to the receiver on
which they impinge, and thus are treated in connection with the
radiator or receiver, that is, the electric conductor, in the theory
of transient electric phenomena and oscillations.*
The radiation may be of a single frequency, that is, a single
wave; or a mixture of different frequencies, that is, a mixture
of different and frequently of an infinite number of waves.
Electric radiation usually is of a single frequency, that is, of the
frequency or wave length determined by the constants of the
electric circuit which produces the radiation, mainly the induct-
ance L and the capacity C. They may, however, have different
wave shapes, that is, comprise, in adolition to the fundamental
wave, higher harmonics or multiples thereof, just as the sound
waves which represent the same tone with different musical
instruments are of the same frequency but of different wave
shapes, that is, contain different higher harmonics.
Light radiations usually are a mixture of a number of waves of
different frequencies, and very commonly a mixture of an infinite
number of frequencies, as is, for instance, the case with the
* "Theory and Calculation of Transient Electric Phenomena and Oscilla-
tions. "
RELATION OF BODIES TO RADIATION. 21
radiation of an incandescent body as a lamp filament, which
contains all the frequencies from long ultra-red waves over
visible light waves to ultra-violet waves.
In the action of vibrations on our senses there is a characteristic
difference between the perception of sound waves by the ear and
that of light waves by the eye : the ear is analytic, that is, can
separate the individual waves in a mixture of different sound
waves, as an accord on the piano, and distinguish the individual
components of the mixed sound which reaches the ear. Thus
we can hear and distinguish an individual voice amongst a mass
of other noises. The eye, however, perceives only the resultant
of all -the visible radiations which reach it, but cannot separate
their components, and very different mixtures of radiations thus
make the same impression upon the eye: thus, for instance,
numerous mixtures of blue and yellow light appear alike to the
eye and the same as green light, that is, appear green, while
physically, it is obvious that mixtures of blue and yellow light
are essentially different from green light.
It is interesting to imagine how nature would look to us if the
eye were analytic, that is, could separate the different component
radiations, and if it could perceive waves over as great a range of
frequency as the ear, about nine octaves instead of less than one
octave as is now the case. The information given to us by the
sense of sight would be infinitely increased, and we would see
many differences and changes which now escape us.
10. However, while the eye cannot distinguish the different
component radiations but sees only their resultant, the specific
effects of the component radiations, as the physiologically harm-
ful action of an ultra-violet component of light, still remain, even
if the eye does not see the components, and in the study of radia-
tion for the purpose of its engineering use for illumination it is
therefore necessary to analyze the mixed radiation given by a
source as a lamp, by resolving it into its component waves.
This is done by using some feature of the radiation which
varies with the frequency. Such is the case with the velocity of
propagation.
The velocity of light in empty space is 3 X 1010 cm. per sec.
It is practically the same in air and other gases. In denser
bodies, however, as water, glass, etc., the velocity of light is less
and, as will be seen, is different for different frequencies.
22
RADIATION, LIGHT, AND ILLUMINATION.
Assume then, in Fig. 15, a beam of light B striking under an
angle the boundary between two media, as air A and water W,
the vibration of the ether particles in the beam of light is at right
angles to the direction of propagation BC, and successively the
waves thus reach at blf a2 bz . . . As soon, however, as the back
edge of the beam reaches the boundary at D its speed changes
FIG. 15.
by entering the medium W — decreases in the present instance.
Let then Sl = speed of propagation in medium A, S2 = speed of
propagation in medium W. Then, while the center of the beam
moves the distance EC, the back edge, in the denser medium,
a
moves only the distance DI = -^EC, and the wave front of the
»i
back half of the beam thus changes to CI while that of the front
half of the beam, which is still in the medium A, remains GC.
Then, while the front edge of the beam moves from G to H, the
center and the whole back half of the beam moves in the denser
o
medium TF, only the distance CK = — 2 GH, and the wave front
«i
of the beam, in the medium TF, now is EL. That is, due to the
difference in velocity in the two media A and W, the wave front
of the beam, and thereby its direction of propagation, is changed
RELATION OF BODIES TO RADIATION. 23
when traversing the boundary between the two media, and the
beam EC continues its motion in the direction CM.
Let then o^ = angle of incidence, that is, the angle between
the incident beam BC and the perpendicular CN on the boundary,
and a2 = angle of refraction, that is, the angle between the out-
going or refracted beam CM and the perpendicular CP on the
boundary. It is then :
FDH = a, and LHD = a2 ;
hence,
FH = DH sin a, and DL = DH sin av (1)
The front edge of the beam moves the distance FH in medium
A, while the back edge moves the distance DL in medium W;
that is,
FH + DL = S, - S3; (2)
hence, substituting (1) into (2), gives:
sin «1 Sl
sn
(3)
That is, the ratio of the sines of the angle of incidence and the
angle of refraction equals the ratio of the speed of propagation
in the two media, hence the ratio of the sines of these two angles
is constant. This is the law of refraction, and this ratio of sines
is called the refractive index between the two media A and W. As
the refractive index of one medium W, then, is understood its re-
fractive index against empty space or against air :
sn a
where S is the velocity of light in empty space = 3 X 1010, and
Sl the velocity in the medium, of which ^ is called the refractive
index.
From equation (4) it follows, that, if ^_2 is the refractive index
between medium 1 and medium 2, £2_3, the refractive index
between medium 2 and medium 3, dl-3 = £2_3 -*- ^_2 = refractive
index of medium 1 and medium 3; that is, the refractive index
between any two media is derived as the ratio of their refractive
indices against a third medium, as, for instance, against air.
24 RADIATION, LIGHT, AND ILLUMINATION.
11. Incidentally, it is interesting to consider the corresponding
relations in electric waves.
In an electric circuit, the speed of propagation of an electric
wave is, when neglecting the energy losses in and by the con-
ductor:
S = -L= , (5)
VLC
where L is the inductance, C the capacity of the conductor per
unit length (the length measured in the same measure as the
speed S).
The inductance L is proportional to the permeability /*, and
the capacity C proportional to the dielectric constant, or specific
capacity K of the medium surrounding the conductor, that is, the
medium through which the electric wave propagates; that is,
A V p*
where A is a proportionality constant.
The ratio of the speed of propagation of an electric wave in two
media 1 and 2 thus is:
<,,
for empty space, fj. = 1 and « = 1;
hence,
(8)
where Sl is the speed of propagation in the medium of constants
/^ and jcr
Comparing equation (8) with (4) it follows :
Vl = d*-, (9)
that is, the square of the refractive index d equals the product of
permeability JJL and dielectric constant K.
Since for most media the permeability /JL = 1, for all except
e maneti mri
the magnetic materials
RELATION OF BODIES TO RADIATION.
25
This relation between the constant of the electric circuit K and
the constant of optics d was one of the first evidences of the
identity of the meclium in which the electric field exists with
the medium which carries the light waves. It is, however, only
approximately correct, as the refractive index d varies with the
frequency and is derived for the extremely high frequencies of
light radiation, while K refers to stationary conditions. A better
agreement is thus reached when using as d the refractive index
extrapolated for infinite wave lengths.
12. It is found that the different component frequencies of a
beam of radiation are deflected differently when passing from one
medium into another, and the higher frequencies are deflected
FIG. 16.
more than the lower frequencies, thus showing that the velocity
of propagation decreases with an increase of frequency, that is,
a decrease of wave length.
This gives a means of resolving a mixed radiation into its com-
ponent waves, that is, into a spectrum, by refraction.
A narrow beam of light B (Fig. 16) is passed through a prism P
of transparent material, and the component frequencies then
appear on the screen A (or are seen by the eye) side by side, the
red R to the left, the violet V to the right, in Fig. 16, and the green
G in the middle.
It is obvious that the material of the prism must be transparent
to the radiation; thus, when studying ultra-violet radiation to
which glass is opaque, glass prisms cannot be used, but some
material transparent to ultra-violet light such as a quartz prism
must be used.
26
RADIATION, LIGHT, AND ILLUMINATION.
The beam of light also can be resolved into its components by
a diffraction grating, in which case the lower frequencies are
deflected more than the higher frequencies ; that is, the red more
than the violet.
These two forms, the refracting spectroscope and the diffract-
ing spectroscope, now enable us to resolve a beam of mixed radia-
tion into its components and thus study its spectrum.
13. I show you here a number of typical spectra:
(1). The spectra of an incandescent lamp and an alcohol
lamp with Welsbach mantel. These are continuous spectra, that
is, show all the radiations from red over orange, yellow, green,
blue, indigo to violet, uniformly shading into each other.
(2a). The spectrum of the mercury lamp. This is a line
spectrum, that is, shows only a finite number of bright lines on
black background. It contains five bright lines ; greenish yellow,
bright green, indigo and two violet, one faint dark green line, and
1 1 1
1 1 1
1 Ij
RED
ORANGE 1 YELLOW 1 GREEN
BLUE
INDIGO
VIOLET
FIG. 17.
a number of very faint red and orange lines, of which three are
indicated dotted in Fig. 17.
(26). The spectrum of an arc between titanium carbide elec-
trodes. This also is a line spectrum, but unlike the mercury
spectrum, which has only six bright lines, the titanium spectrum
contains many thousands of bright lines, so that with the low
power of the spectroscope which you have, the lines blurr into
each other and we see only the most prominent or brightest lines
on a uniformly luminous background, which latter requires a
more powerful spectroscope to resolve into lines.
(3) . The band spectrum. This shows a number of bright bands,
frequently gradually fading out at their edge and separated by
dark spaces. It thus differs from the continuous spectrum (1) in
being discontinuous, that is, missing certain ranges of frequency,
and differs from the line spectrum (2) in that the band spectrum
has a number or range of frequencies in each band, where the line
RELATION OF BODIES TO RADIATION. 27
spectrum has only 'one single frequency in each line. Such
band spectra are usually characteristic of luminescent compounds
or of gases and vapors at high pressure, while elementary gases
or vapors give line spectra. Absorption and fluorescence also
give band spectra, and I thus show you a band spectrum by opera-
ting a mercury lamp in a tube of uranium glass, behind a trans-
parent screen colored by rhodamine (an aniline dye which
fluoresces red). As you see, the spectrum shows a broad red
band, due to the reddish screen, and a greenish yellow band due
to the uranium glass, while the normal mercury lines are de-
creased in intensity.
(4). If you now look with the spectroscope at the Welsbach
mantel through the mercury arc stream, you see the continuous
spectrum of the mantel and superimposed upon it the line spec-
trum of the mercury lamp. The light giving mercury vapor thus
is transparent for the light of the Welsbach mantel back of it, and
lets it pass through, with the exception of those particular fre-
quencies which it gives itself; that is, a luminous gas absorbs
those frequencies of radiation which it produces, but is trans-
parent for all other frequencies. This is easily understood: an
atom on which a vibration impinges will be set in motion by it
and thus absorb the energy of the impinging vibration if it is able
to vibrate with the frequency of the impinging vibration; that is,
to resonate with it, but will not be affected by any other frequency
to which it cannot respond, and thus is transparent to all frequen-
cies of vibration, except to those to which it can respond; that is,
which it produces when vibrating.
When looking at a continuous spectrum through a luminous
gas or vapor, two cases thus may occur: either the spectrum lines
of the gas are brighter than the continuous spectrum, as in the
present case, and then appear as bright lines on a bright back-
ground, or the continuous spectrum is brighter than the lines of
the gas spectrum in front of it and the lines of the gas spectrum
appear less bright than the background, that is, appear as dark
lines on a bright background. Such a spectrum is called a
reversed spectrum, or absorption spectrum. It shows the lines of
the gas or vapor spectrum, by contrast, dark on the brighter back-
ground of the continuous spectrum.
The sun and many fixed stars present such a reversed spectrum :
the sun's spectrum shows the spectrum lines of all the elements
28
RADIATION, LIGHT, AND ILLUMINATION.
which are in the sun's atmosphere as dark lines on the continuous
spectrum given by the inner core of the sun.
Whether the line spectrum of a gas or vapor is reversed by the
continuous spectrum of a solid or liquid back of it or not depends
upon the relative intensity, and thus, to some extent, on the rela-
tive temperature. Some fixed stars show bright lines on a less
luminous background, due possibly to a higher temperature and
greater thickness of their atmosphere, and sometimes bright lines
and dark lines occur simultaneously, or dark lines may change to
bright lines at such places at which, by some activity, as a tem-
perature rise, their brilliancy is greatly increased.
FIG. 18.
Combinations of the different types of spectra: continuous
spectrum, line spectrum, band spectrum, reversed spectrum,
frequently occur, as we have seen bands and lines together in the
modified mercury spectrum, and in this case, by turning on an
incandescent lamp, we can still add a continuous spectrum due
to the light of the incandescent lamp reflected from the walls of
the room. So also in the continuous spectrum of incandescent
bodies, bright bands or dark bands occasionally appear, that is,
regions in the spectrum of greater or lesser intensity, as will be
discussed in the paragraphs on colored radiation and selective
radiation.
RELATION OF BODIES TO RADIATION.
29
14. When a beam of radiation impinges upon a body it is
resolved into three parts : one part is reflected, that is, does not
enter the body at all, but is thrown back. The second part is
absorbed in the body, that is, converted into another form of
energy (which other form of energy usually is heat, but may be
chemical energy, some other frequency of radiation, etc.) and the
third part is transmitted, that is, passes through the body, and
out of it, if the body is not too thick. No body reflects, or
absorbs, or transmits all the radiations, but even the most per-
fectly reflecting body absorbs and transmits some radiation, the
most transparent body reflects and absorbs some radiation, etc.
Reflection may be either regular reflection, or irregular reflec-
tion. In the former case (Fig. 18) the beam of light is reflected
under the same angle under which it impinges upon the body,
and the body thus acts as a mirror, that is, gives a virtual image
FIG. 19.
back of it as shown in dotted line in Fig. 18. In the latter case
(Fig. 19) the light is reflected irregularly in all directions.
A body which reflects all the frequencies of radiation uniformly,
that is, in which the percentage of the impinging radiation, which
is reflected, is the same for all frequencies of radiation, is called a
colorless body, and a body which reflects a higher percentage of the
radiation of some frequency than of other frequencies, is called
a colored body, and its color is the color of radiation, that is,
the frequency or frequencies which it reflects more than other
frequencies.
A colorless body which reflects all the radiation impinging upon
it is called a white body. Most nearly white bodies are silver,
magnesia, chalk, etc. A body which reflects none of the radiation
impinging upon it, but absorbs all, is called a block body. The
30 RADIATION, LIGHT, AND ILLUMINATION.
most nearly black bodies are lampblack, charcoal, etc. A body
which reflects a constant part of the impinging radiation, that is,
the same part or percentage for all frequencies, is called a grey
body, and the ratio of the reflected light to the total impinging
light is called its whiteness or albedo. A perfectly white body
thus has albedo 1, a perfectly black body albedo 0, and a body
which reflects one-quarter and absorbs the other three-quarters
of the radiation of any wave length impinging upon it, would be
said to have albedo 0.25.
Black, white and grey thus are not considered as colors in
physics.
As examples of colorless bodies I show you here :
Regular reflection: polished silver, white; polished iron, grey.
Irregular reflection: powdered magnesia, white; lampblack,
black; powdered zinc, barium sulphide, grey.
As example of colored bodies I show you :
Regular reflection: polished copper, red; polished gold or
brass, yellow.
Irregular reflection: mercury sulphide (cinnabar), red; potas-
sium bichromate, orange; magnesium chromate, yellow; copper
acetate-arsenite (paris green), green; copper oxide hydrate
precipitated by ammonia, blue; ultra-marine, indigo ; magnesium
permanganate mixed with magnesia, violet.
15. Of the radiation which enters a body, that part which is
absorbed is usually converted into heat. Thus a black body,
when exposed to radiation, becomes hotter than a white body,
which reflects, or a transparent body, which transmits, most
of the radiation. Thus the globe of a colored incandescent lamp,
which absorbs more of the radiation than a transparent globe,
becomes hotter than a clear glass globe. When scattering dirt
on the snow it can be made to melt down far more rapidly in the
spring, under the rays of the sun, than when remaining clean, etc.
Some bodies convert the absorbed radiation into chemical
energy, into other frequencies of radiation, etc.
Bodies which convert the absorbed radiation, or rather a part
thereof, into radiation of different, as far as known always
lower, frequencies, are called fluorescent bodies. Thus the solu-
tion of rhodamine in alcohol, which I show you here, fluoresces
red. It transmits red light, but absorbs green, blue and violet
light, and converts a part thereof into red light. This is best
RELATION OF BODIES TO RADIATION. 31
illustrated by exhibiting it in a source of light which contains no
red rays, as the mercury lamp. You see in the rays of the mer-
cury lamp the rhodamine solution looks bright red, the red light
seems to come from the inside of it, and especially through a red
glass the solution looks like a red hot incandescent body. Here
then, as no red light reaches the solution, the red light given by it
must be produced by frequency conversion from other radiation.
The spectroscope shows especially the bright green mercury line
weakened.
The phenomena of conversion of absorbed light into other
forms of energy will be more fully discussed in the following
paragraphs.
16. By the transmitted light, that is, the radiation which
passes through them, bodies are again divided into colorless
bodies; that is, such bodies which transmit the same percentage
of radiation for every wave length or frequency, and colored
bodies; that is, bodies which transmit a larger percentage of
radiation of some frequencies than of others, and as the trans-
parent color of a body, then, is understood the color, that is, the
frequency, of that radiation of which the greatest percentage is
transmitted. Thus a red glass is one which transmits a higher
percentage of red radiation than of any other radiation.
A body, then, is called transparent, if it transmits all the radia-
tion, and opaque, if it transmits no radiation, but absorbs or
reflects all. If only a part of the radiation is transmitted, but
in such manner that it is the same part for all frequencies, the
body is called grey; or imperfectly transparent, if the part which
is not transmitted is absorbed in the body ; and translucent, if
the part which is not transmitted is irregularly reflected inside
of the body.
The most perfectly transparent bodies, for visible light, are
glass, water, quartz, etc. ; the most opaque are the metals, and
perfectly, or almost perfectly opaque are the magnetic metals,
perhaps due to the very low speed of propagation in these metals,
which would result from the high value of the permeability /* by
equation (8) paragraph 11.
As example of colorless bodies I show you here a glass tube
filled with water, transparent; a tube filled with nigrosine solu-
tion in alcohol, opaque and black; a very diluted solution of
nigrosine with traces of other aniline dye for color correction, in
32 RADIATION, LIGHT, AND ILLUMINATION.
alcohol, as grey, and a tube filled with an emulsion of water with
a solution of chloroform in white paraffin oil, which latter solu-
tion has the same specific gravity as water, translucent.
Samples of transparent colored bodies are: carmine solution,
red; potassium bichromate solution, orange; potassium chromate
solution, yellow; nickel sulphate solution, green; copper nitrate
solution, blue; diluted potassium permanganate solution, or
diluted solution of iodine in chloroform, violet.
As seen, the terms " colorless" and " colored" have two dif-
ferent meanings when applied to the reflected radiation and
when applied to the transmitted radiation, and the color of a
body in reflected light may be different, and frequently is differ-
ent, from its color in transmitted light, and some bodies may be
colorless in reflected light, but colored in transmitted light, and
inversely. In materials of low absorption, the transmitted and
the reflected colors must be approximately complimentary ; thus
the transmitted color of the atmosphere is orange, the reflected
color blue.
17. Colors are, therefore, distinguished into opaque colors and
transparent colors. The opaque colors are those shown by the
light reflected from the body, the transparent colors those shown
by the light transmitted through the body. In reflected light,
the transparent colors, therefore, show only when covering a
white, that is, reflecting surface, and then, due to the light
reflected from the white background of the transparent coloring
body traversing this body twice, before and after reflection, and,
therefore, depend in their brilliancy on the background. The
difference between opaque and transparent colors, the former
reflecting from the surface, the latter reflecting from back of
the colored substance, is seen by comparing the appearance of
the two classes of colors shown in 14 and in 16.
In its general use, the terms colorless, white, black, transparent,
opaque, refer only to the visible radiation, that is, to the frequen-
cies within that octave which the eye perceives as light. More
broadly, however, these terms may in physics be applied to the
total range of radiation, and then many substances which are
colorless for visible light, would be considered as strongly colored,
that is, show for different frequencies great differences in the per-
centage of radiation which they reflect or transmit. Thus we
have seen that glass, which is transparent for visible light, is
RELATION OF BODIES TO RADIATION. 33
entirely opaque for some ultra-violet light and also opaque for
ultra-red light of low frequency, so in this broader sense would
have to be called colored* the color of clear glass, however, is that
of the visible spectrum; or, for instance, iodine solution, which is
opaque for visible light, is transparent for ultra-red light, that is,
its color is ultra-red, etc.
In this broader sense, referring to the total range and not
merely to the visible range, glass, water, mica, etc., are not color-
less transparent but colored, and quartz is probably the most
transparent and colorless body.
18. The color of the body, thus, is represented by that fre-
quency or those frequencies. of radiation of which a higher per-
centage are reflected or transmitted than of the other frequencies
of radiation. This color, therefore, is a characteristic property
of the body and independent of the character of the light and of
its physiological effect on the eye, and can thus be called the
actual or objective color of the body. If we consider diffused
daylight as white, then the body appears to the eye in its
objective or actual color when compared with a white body,
that is, a body uniformly reflecting all radiation in the diffused
daylight. Under other conditions, as, for instance, in artificial
illumination, bodies do not always appear to the eye in their
objective colors, but may show a very different color depending
on the character of the source of light. For instance, I have
here a plate of colored glass : looking through it at the mercury
lamp you see the glass has an olive green color; but when I turn
on an incandescent lamp you see that it is ordinary red glass.
Its objective color is red, its subjective color in the mercury
light is green. Looking through this glass in daylight it
appears red as it transmits more red light than other colors of
light, and the transmitted light thus contains a higher per-
centage of red rays than diffused daylight. The rays of the
mercury lamp, however, contain very little red light and very
much green light, and while by this red glass a much higher
percentage of the red light from the mercury lamp is trans-
mitted than of its green light, this higher percentage of trans-
mitted red light is very much less than the lower percentage of
the transmitted green light, and, therefore, in the transmitted
light, green still preponderates more than in the diffused day-
light, that is, the glass appears green. For instance, if in the
34 RADIATION, LIGHT, AND ILLUMINATION.
mercury lamp the ratio of red light to green light is only one
hundredth of what it is in daylight, and the red glass transmits
ten times as high a percentage of red as of green light, then in
the light of the mercury lamp transmitted through this red glass
the ratio of red light to green light is still only one-tenth of what
it is in daylight, and the glass thus appears green.
We have to distinguish between the actual or objective color of a
body, which is a constant of the body, and its apparent or sub-
jective color, which depends upon the light in which we view the
body, and therefore may be very different for different illumi-
nants, and bodies which have the same colors in one illuminant
may have entirely different colors in another illuminant and
inversely. It is, however, the subjective color of the body cor-
responding to the particular illuminant used which we see, and
which is, therefore, of importance in illuminating engineering,
and the study of the subjective colors, therefore, is of foremost
importance, and the success or failure of an illumination depends
on the production of the desired subjective colors.
19. Broadly, an illumination discriminates for the color in
which it is deficient and the color in which it is rich. The color
in which the illuminant is deficient — as red in the mercury lamp,
blue and violet in the incandescent lamp — appears black; the
color in which the illuminant is abnormally rich — as yellow in
the incandescent lamp, green in the mercury lamp — appears as
white ; that is, both colors disappear, more or less ; as colors, be-
come colorless. Thus in the yellow incandescent lamp, opaque
yellow appears the same as white, opaque blue and violet appear
more or less as black; transparent yellow appears colorless, trans-
parent blue and violet appear colorless and from light transparent
grey to opaque black. In the green mercury lamp, opaque green
and white appear the same, opaque red appears as black; trans-
parent green appears colorless, and transparent red appears
colorless, from clear transparent to grey, to opaque black, de-
pending upon its intensity.
It is interesting to see the difference between opaque and
transparent colors in this respect: as opaque colors the deficient
color turns black, the excess color white; but as transparent
colors both become colorless and more or less transparent. Thus,
in the mercury lamp, red and green as transparent colors both
vanish, or rather, very greatly decrease in their prominence.
RELATION OF BODIES TO RADIATION. 35
As the eye perceives only the resultant of radiation, very dif-
ferent combinations of radiation may give the same impression
to the eye, but when blotting out certain radiations, as red and
green, in the mercury lamp, these different combinations of radia-
tion may not give the same resultant any more, that is, become
of different colors, and inversely, different colors, which differ
only by such component radiations as are blotted out by an
illuminant, become equal in this illuminant. For instance, a
mixture of red and blue, as a diluted potassium permanganate
solution, appears violet in daylight. In the mercury light it
appears blue, as the red is blotted out, and in the light of the
incandescent lamp it appears red, as the blue is blotted out.
I show you here, in the light of an incandescent lamp, two
pieces of black velvet. I turn off the incandescent lamp and
turn on the mercury lamp, and you see the one piece is blue, and
the other black. Now I show you two pieces of brownish black
cloth in the mercury light. Changing to the incandescent lamp
you see that the one is a bright crimson, and the other still practi-
cally black. In both cases the color deficient in the illuminant
appeared as black.
This tube of copper chloride crystals appears bright green in
the incandescent lamp. In the mercury light it is a dirty white.
The excess color, green, is blotted out.
These crystals of didymium nitrate, which are a faint light
pink in daylight, are dark pink in the incandescent light. In
the mercury light they are blue : the color is a mixture of red and
blue, and the one is blotted out in the mercury light and the other
in the incandescent light.
These two tubes, one containing a concentrated solution of
manganese chloride, the other a solution of didymium nitrate, are
both a dark pink in the incandescent light. In the mercury
light the first becomes a very faint pink, the second becomes grass
green.
These tubes, one containing a solution of didymium nitrate, the
other a diluted solution of nickel sulphate, appear both light green
in the mercury light. In the incandescent lamp the former is
dark pink, the latter dark green. [Didymium, which formerly
was considered as an element, has been resolved into two ele-
ments, praseodymium, which gives green salts, and neodymium,
which gives pink salts. It is interesting to see that this separa-
36 RADIATION, LIGHT, AND ILLUMINATION.
tion is carried out photometrically by the light: the mercury
lamp showing only the green color of the praseodymium, the
incandescent lamp the pink color of neodymium].
I have here a number of tubes, which seen in the light of
the incandescent lamp contain red solutions of nearly the same
shade. Changing to the mercury lamp you see that they exhibit
almost any color. As the red disappeared in the mercury lamp
the other component colors, which did not show in the incandes-
cent lamp as they were very much less in intensity than the red,
now predominate : potassium permanganate solution turns blue,
carmine blue ; potassium bichromate, greenish brown ; coralline,
(an aniline dye), olive green, etc., etc.
Again, a number of tubes, which in the mercury light appear of
the same or nearly the same blue color, turn to very different
colors when seen in the incandescent lamp, due to the appearance
of red and green, which were not seen with the mercury light.
A solution of rhodamine, however, which looks a dull red in the
light of the incandescent lamp, turns a glowing crimson in the
mercury lamp, due to its red fluorescence. This diluted solution
of rhodamine and methyl green (aniline dyes), which is grey in the
light of the incandescent lamp, turns brownish red in the mercury
lamp, the green is blotted out, while the rhodamine shows its
red fluorescence. Thus, you see, the already very difficult prob-
lem of judging the subjective colors of bodies under different illu-
minants is still greatly increased by phenomena as fluorescence.
To conclude then : we have to distinguish between colorless and
colored bodies, between opaque colors and transparent colors,
between color, as referred to the visible range of radiation only,
or to the total range, including ultra-red and ultra-violet, and
especially we have to realize the distinction between objective or
actual color, and between subjective or apparent color, when
dealing with problems of illuminating engineering.
LECTURE III.
PHYSIOLOGICAL EFFECTS OF RADIATION.
Visibility.
20. The most important physiological effect is the visibility of
the narrow range of radiation, of less than one octave, between
wave length 76 X 10~6 and 39 X 1Q-6.
The range of intensity of illumination, over which the eye can
see with practically equal comfort, is enormous: the average
intensity of illumination at noon of a sunny day is nearly one
million times greater than the illumination given by the full moon,
and still we can see fairly well in either case; that is, the human
eye can adapt itself to enormous differences in the intensity of
illumination, and that so perfectly that it is difficult to realize the
differences in intensity without measuring them. The photo-
graphic camera realizes it. An exposure taken in T^ second
with TV opening of the diaphragm in full sunlight usually gives a
better photograph than an exposure of 10 minutes at full opening,
in the light of the full moon. The ratio of time of exposure in
the two cases, however, is about 1 to 1,000,000, thus showing the
difference in the intensity of illumination. Also, the disk of the
moon, when seen in daylight, has about the same intensity as the
sky — somewhat more than the cloudless sky, less than white
reflecting clouds. As the surface of the moon's disk, of one-half
degree diameter, is about TffsWtf the surface of the sky, it thus
follows that the daylight reflected from the sky is about 100,000
times more intense than the light of the full moon.
The organ by which we perceive the radiation, the human eye
(Fig. 20), contains all the elements of a modern photographic
camera — an achromatic lense: the lense L, of high refractive
power, enclosed between the two transparent liquids A and B
which correct the color dispersion, that is, give the achromatic
property; a diaphragm: the iris 7, which allows the increase or
decrease of the opening P, the pupil; a shutter: the eyelids and
87
38 RADIATION, LIGHT, AND ILLUMINATION
the sensitive plate or retina R. The nerves of vision end at the
back of the retina, and in the center of the retina is a spot F,
the "sensitive spot " or " fova," at which
the retina is very thin, and the nerve
ends specially plentiful. At this spot we
thus see sharpest and clearest, and it is
this spot we use for seeing by turning
the eye so as to fix on it the image of
the subject we desire to see, while the
image on the rest of the retina is used
merely for orientation.
The adaptability to the enormous
FIG. 20. range of intensity of illumination, which
as seen we meet in nature, is secured:
(1). By changing the opening and thereby the amount of light
admitted to the eye, by contracting or opening the pupil P. This
action is automatic. In low intensity of illumination the pupil
thus is wide open and contracts at higher intensities. As this
automatic action takes an appreciable, though short time, a flash
light photograph shows the pupil of the eye fully open and thereby
gives a staring impression to the faces which is avoided by keep-
ing a photographically inactive light, as a candle, burning outside
of the field of the camera when preparing for a flash light photo-
graph.
(2). By the fatigue of the optic nerves, exposed to high inten-
sity of illumination, the nerves becomes less sensitive, while at
low intensity they rest and thus become more sensitive, and the
differences of sensation are hereby made very much less than
corresponds to the differences of intensity of radiation. There-
fore, when entering a brightly illuminated room from the dark-
ness we are blinded in the first moment, until the eye gets
accustomed to the light, that is, the nerves become fatigued and
so reduce the sensation of light. Inversely, when stepping from
a bright room into the darkness we first see almost nothing until
the eye gets accustomed to the darkness, that is, the nerves of
vision are rested and their sensitivity thus increased so as to per-
ceive the much lower intensity of illumination.
(3). By the logarithmic law of sensation. The impression made
on our senses, eye, ear, etc., that is, the sensation, is not propor-
tional to the energy which produces the sensation, that is, the
PHYSIOLOGICAL EFFECTS OF RADIATION. 39
intensity of the light, the sound, etc., but is approximately
proportional to its logarithm and the sensation, therefore,
changes very much less than the intensity of light, etc., which
causes the sensation. Thus a change of intensity from 1 to
1000 is 1000 times as great a change of intensity as from
1 to 2, but the change of sensation in the first case, log 1000 = 3,
is only about 10 times as great as the change in the latter case,
log 2 - 0.301.
This logarithmic law of sensation (Fechner's Law), while usu-
ally not clearly formulated, is fully familiar to everybody, is con-
tinuously used in life, and has been used from practical experience
since by-gone ages. It means that the same relative or percent-
age change in intensity of light, sound, etc., gives the same change
of sensation, or in other words, doubling the intensity gives the
same change in sensation, whether it is a change of intensity from
one candle power to two candle power, or from 10 to 20, or from
1000 to 2000 candle power.
It is obvious that the change of sensation is not proportional to
the change of intensity; a change of intensity of light by one
candle power gives a very marked change of sensation, if it is a
change from one to two candle power, but is unnoticeable, if it is a
change from 100 to 101 candle power. The change of sensation
thus is not proportional to the absolute change of intensity — one
candle power in either case — but to the relative or percentage
change of intensity, and as this is 100 per cent in the first, 1 per
cent in the latter case, the change of sensation is marked in the
first, unnoticeable in the latter case.
This law of sensation we continuously rely upon in practice.
For instance, when designing an electrical distribution system for
lighting, we consider that the variation of voltage by 1 per cent is
permissible as it gives a change of candle power of about 5 per
cent, and 5 per cent variation is not seriously noticeable to the eye.
Now this 5 per cent change of candle power may be a change from
1 to 0.95, or by -fa candle power, or it may be a change from 1000
to 950, or by 50 candle power, and both changes we assume, and
are justified herein from practical experience, to give the same
change of sensation, that is, to be near the limits of permissi-
bility.
This law of sensation (Fechner's Law) means :
If i = intensity of illumination, as physical quantity, that is,
40 RADIATION, LIGHT, AND ILLUMINATION.
in meter-candles or in watts radiation of specified wave length,
the physiological effect given thereby is :
L = A log V
%>
where A is a proportionality constant (depending on the physio-
logical measure of L) and \ is the minimum perceptible value of
illumination or the "threshold value," below which sensation
ceases.
The minimum value of change of intensity i, which is still
just perceptible to the average human eye, is 1.6 per cent. This,
then, is the sensitivity limit of the human eye for changes of
illumination.
Obviously, when approaching the threshold value i0, the sensi-
tivity of the eye for intensity changes decreases.
The result of this law of sensation is that the physiological effect
is not proportional to the physical effect, as exerted, for instance,
on the photographic plate. The range of intensities permissible
on the same photographic plate, therefore, is far more restricted.
A variation of illumination within the field of vision of 1 to 1000,
as between the ground and the sky, would not be seriously felt by
the eye, that is, not give a very great difference in the sensation.
On the photographic plate, the brighter portions would show 1000
times more effect than the darker portions and thus give bad
halation while the latter are still under exposed. A photographic
plate, therefore, requires much smaller variations of intensity in
the field of vision than permissible to the eye. In the same man-
ner the variations of intensity of the voice, used in speaking, are
far beyond the range of impression which the phonograph cylin-
der can record, and when speaking into the phonograph a more
uniform intensity of the voice is required to produce the record,
otherwise the lower portions of the speech are not recorded, while
at the louder portions the recording point jumps and the voice
breaks in the reproduction.
21. The sensitivity of the eye to radiation obviously changes
with the frequency, as it is zero in the ultra-red, and in the ultra-
violet — where the radiation is not visible — and thus gradually
increases from zero at the red end of the spectrum to a maximum
somewhere near the middle of the spectrum and then decreases
again to zero at the violet end of the spectrum; that is, the physi-
PHYSIOLOGICAL EFFECTS OF RADIATION.
41
ological effect produced by the same radiation power — as one
watt of radiating power — is a maximum near the middle of the
visible spectrum and decreases to zero at the two ends, about as
illustrated by the curves in Fig. 21. Inversely, the mechanical
equivalent of light, or the power required to produce the same
physiological effect — as one candle power of light — is a maxi-
mum near the middle of the spectrum and decreases from
there to infinity at the end of the visible range, being infinite
RED
YELLOW
GREEN
BLUE
VIOLET
FIG. 21.
in the ultra-red and ultra-violet, where no power of radiation can
produce visibility. It thus varies about as indicated in Fig. 22.
The mechanical power equivalent of light, thus, is not constant,
as the mechanical energy equivalent of heat — which is 426 kgm.
or 4.25 kile-joule per calorie — but is a function of the frequency,
that is, of the color of radiation, with a maximum, probably not
very far from 0.01 watt per candle power in the middle of the
spectrum.
When comparing, however, the physiological effects of different
frequencies of radiation, that is, different colors of light, the diffi-
culty arises that different colored lights cannot be compared
photometrically, as all photometers are based on making the illu-
mination produced by the two different sources of light equal, and
when these sources of light are of different color they can never
become equal. As long as the colors are not very different -
two different shades of yellow or yellowish white and white — the
eye can still approximately estimate the equality of intensity and
42
RADIATION, LIGHT, AND ILLUMINATION.
thus compare them, though not as accurately as when the two
sources of light are of the same color. With very great color
differences, as green light and orange light, this is no longer
feasible. However, an accurate comparison can still be made on
the basis of equal ease in distinguishing objects. As the pur-
FIG. 22.
pose for which light is used is to distinguish objects, the correct
comparison of lights obviously is on the basis of equal distinctness
of objects illuminated by them; that is, two lights, regardless
whether of the same or of different colors, give the same candle
power, that is, the same physiological effect, if they enable us to
distinguish objects with the same ease at the same distance.
Experience has shown that the sharpest distinction, that is, the
greatest accuracy in comparing different lights in this manner, is
reached by determining the distance from the source of light at
PHYSIOLOGICAL EFFECTS OF RADIATION. 43
which print of moderate size just ceases to be readable. For this
purpose the print must be a mixture of letters which do not form
intelligible words and the point which can be determined most
accurately is where large letters, as capitals, are still readable,
while small letters are already unreadable (see p. 174) . Obviously,
in comparing different colors of light the object must be colorless,
that is, the print be black on white. This method of comparison
of the physiological effect, by what has been called the "lumino-
meter," is theoretically the most correct, as it is independent of
the color of light. It is, however, not as accurate as the compari-
son by photometer, and thus the average of a number of observa-
tions must be used. The only error which this method leaves is
that due to the difference in the sensitivity of different eyes, that
is, due to the differences between the sensitivity curves (Fig. 21),
and this in most cases seems to be very small.
22. It is found, however, that the sensitivity curve for different
colors of radiation is a function of the intensity of radiation; that
is, the maximum sensitivity point of the eye is not at a definite
frequency or wave length, but varies with the intensity of illumi-
nation and shifts more towards the red end of the spectrum for
high, towards the violet end of the spectrum for low intensity of
illumination, and for illumination of very high intensity the maxi-
mum physiological effect takes place in the yellow light, while for
very low intensity of illumination it occurs in the bluish green
light; that is, at high intensity yellow light requires less power
for the same physiological effect than any other color of light,
while for low intensity, bluish green light requires less power for
the same physiological effect than any other color of light. Thus,
if an orange yellow light, as a flame carbon arc, and a bluish green
light, as a mercury lamp, appear of the same intensity from the
distance of 100 feet, by going nearer to the lamps the orange
yellow appears to increase more rapidly in intensity than the
bluish green, and from a very short distance the former appears
glaring bright, while the latter is disappointing by not showing
anywhere near the same apparent intensity. Inversely, when
going further and further away from the two lamps the orange
yellow light seems to fade out more rapidly than the bluish green,
and has practically disappeared while the bluish green is still
markedly visible. A mercury lamp, therefore, can be seen from
distances from which a much brighter yellow flame arc is practi-
44
RADIATION, LIGHT, AND ILLUMINATION.
cally invisible, but inversely, from a very short distance the
yellow light appears dazzling, while a mercury lamp of higher
candle power appears less bright.
Fig. 23 illustrates the change of sensitivity with intensity, by
approximate curves of the variation of the relative sensitivity of
the average human eye with the intensity i of illumination in
v
FIG. 23.
meter candles (or rather log i) as abscissas, for red light, wave
length 65.0; orange yellow light, wave length 59; bluish green
light, wave length 50.5; and violet light, wave length 45.0.
As seen for red light as well as violet light — the two ends of
the visible spectrum — the sensitivity is low, while for orange
yellow as well as bluish green light — near the middle of the
visible range — the sensitivity is high.
For bluish green light, however, the sensitivity is high at low
and moderate intensities but falls off for high intensities, while
for orange yellow light the sensitivity is high at high intensities
and falls off at medium and low intensities and ultimately vanishes,
that is, becomes invisible at intensities many times higher than
those at which green light is still well visible.
Red light vanishes from visibility still earlier than orange yel-
low light, while violet light remains visible even at very low
intensities.
The vanishing points of the different colors of light, that is,
PHYSIOLOGICAL EFFECTS OF RADIATION. 45
the minimum intensities which can just be perceived are, approxi-
mately, at:
Color red orange yellow green blue violet
Wave length lw = 67 60.5 57.5 50.5 47 . 43 x 10~fl
Meter-candles in-
tensity .... i0 = 0.06 0.0056 0.0029 0.00017 0.00012 0.00012
Relative radiation
power po = 10,000 1000 100 1 2 20
That is, the minimum visible amount of green light represents
the least amount of power; the minimum visible amount of
blue light requires twice as much power as green light; violet
light 20 times as much, but yellow light 100 times and red light
even 10,000 times as much power as green light at the threshold
of visibility.
While the intensity of radiation varies inversely proportional
to the square of the distance, it follows herefrom that the physio-
logical effect of radiation does not vary exactly with the square
of the distance, but varies somewhat faster, that is, with a higher
power of the distance for orange yellow or the long-wave end of
the spectrum, and somewhat slower, that is, with a lesser power
of the distance than the square, for bluish green or the short-wave
end of the spectrum.
This phenomenon is appreciable even when comparing the
enclosed alternating carbon arc with the open direct current car-
bon arc : by photometer, where a fairly high intensity of illumi-
nation is used, the relative intensity of the two arcs is found
somewhat different than by luminometer, that is, by reading
distances nearer the lower limit of visibility. For low intensities,
the alternating arc compares more favorably than for high
intensities.
It follows, therefore, that in the photometric comparison of
illuminants, where appreciable color differences exist, the inten-
sity of illumination at which the comparison is made must be
given, as it influences the result, or the candle power and the
distance of observation stated.
23. Not only the sensitivity maximum is different for low and
for high intensity of illumination, but the shape of the sensi-
tivity curve also is altered, and for low intensity is more peaked,
that is, the sensitivity decreases more rapidly from a maximum
towards the ends- of the spectrum than it does for high intensity
46
RADIATION, LIGHT, AND ILLUMINATION.
of illumination as indicated by the curves in Fig. 24 which
shows approximate sensitivity curves of the average human eye :
(a) for every low illumination near the treshold value of visi-
bility or 0.001 meter-candles; (b) for medium illumination, 4.6
meter-candles; (c) for very high illumination, 600 meter-candles.
lu,*-. 1.65
I = 45.0
1.70
50.0
L
t
\
\
\
FIG. 24.
(1 meter-candle is the illumination produced by 1 candle power
of light intensity at 1 meter distance; N meter-candles, thus, the
illumination produced by a light source of N candle power at 1
meter distance or of 1 candle power at— -= meter distance, etc.).
VN
As seen, curve (a) ends at wave length /„, = 61 X 10~fl; that is,
for longer waves or orange and red light, 0.001 meter-candles is
below the threshold value of visibility, hence is no longer visible.
The maximum visibility, that is the sensitivity maximum of
the human eye, lies at wave length.
Z0 = 51.1, bluish green for very low intensity, curve (a).
Z0 = 53.7, yellowish green for medium intensity, curve (b).
10 = 56.5, yellow for high intensity, curve (c).
The sensitivity maximum varies with the intensity about as
shown in Fig. 25; that is, it is constant in the bluish green for
low intensities, changes at medium intensities in the range be-
tween 0.5 and 50 meter-candles and again remains constant in
the yellow for still higher intensities.
PHYSIOLOGICAL EFFECTS OF RADIATION.
47
The sensitivity curves, as given in Fig. 24, have the general
character of probability curves :
where lwo is the wave length at maximum sensitivity and HQ is
the sensitivity at this wave length, that is, the maximum sensi-
tivity and ks is a constant which is approximately 120 for low,
LOG
t= -
3
I2
-
1
0
*
1
+
a
4
3 57
- 0.
X)l
0.
bi
0
i
1
1
1
^1
)0
100
^x
ME
s
ER-C,
NDLE
'/
';\
V
/
/
Sr,
H=H<
«•*•
(j*~
i)2
^s
>c
*~- ,
/
[gg
S
FIG. 25.
62 for high intensities and changes in approximately the same
range of intensities in which lwo changes; ks is also plotted in
Fig. 25.
This effect of the intensity of illumination on the sensitivity of
the eye is very important in illuminating engineering as it deter-
mines the color shades which are most effective for the particular
purpose. For instance, in sending the light to great distances,
for signalling, etc., the bluish green of the mercury lamp is best
suited, carries farthest, and the yellow flame arc the poorest; the
white carbon arc superior to the yellow flame arc, even where the
latter is of greater intensity. Inversely, where a big glare of
light is desired, as for decorative purposes, for advertising, etc.,
the yellow flame carbon arc is best suited, the bluish green mer-
cury lamp disappointing.
Apparent exceptions may exist : for instance, the long waves of
the orange yellow penetrate fog better than the short waves of
bluish green, and for lighthouses, where the important problem is
to reach the greatest possible distance in fog, yellow light, thus,
may be superior. In general, however, the bluish green is superior
48 RADIATION, LIGHT, AND ILLUMINATION.
in visibility to the orange yellow for long distances, and inversely,
the orange yellow is superior for short distances.
At the limits of visibility the eye is very many times more
sensitive to green light and, in general, high-frequency light, than
to orange yellow and, in general, low-frequency light.
A necessary result of the higher sensitivity of the eye for green
light is the preponderance of green in gas and vapor spectra. As
no special reason exists why spectrum lines should appear more
frequently at one wave length than at any other and as the radia-
tion is most visible in the green, this explains, somewhat, the
tendency of most highly efficient illuminants towards a greenish
or yellow color (as, for instance, the Welsbach mantel, the Nernst
lamp, etc.).
Pathological and Other Effects on the Eye.
24. Radiation is a form of energy, and thus, when intercepted
and absorbed, disappears as radiation by conversion into another
form of energy, usually heat. Thus the light which enters the
eye is converted into heat, and if its power is considerable it may
be harmful or even destructive, causing inflammation or burns.
This harmful effect of excessive radiation is not incident to any
particular frequency, but inherent in radiation as a form of
energy. It is, therefore, greatest for the same physiological effect,
that is, the same amount of visibility, for those frequencies of
light which have the lowest visibility or highest power equiva-
lent, that is, for the red and the violet and least for the green and
the yellow, which for the same amount of visibility represent
least power. Hence, green and greenish yellow light are the most
harmless, the least irritating to the eye, as they represent the
least power. We feel this effect and express it by speaking of
the green light as "cold light" and of the red and orange light as
"hot" or "warm." The harmful effect of working very much
under artificial illumination is largely due to this energy effect,
incident to the large amount of orange, red, and especially ultra-
red in the radiation of the incandescent bodies used for illumi-
nants and thus does not exist with "cold light," as the light of
the mercury lamp.
Blue and violet light, however, are just as energetic, or "hot,"
as orange and red light, and the reason that they are usually not
recognized as such is that we have no means to produce efficiently
PHYSIOLOGICAL EFFECTS OF RADIATION.
49
powerful blue and violet light, and if we could produce it would
not be able to use it for illumination, due to the specific effects of
this light which will be described in the following.
If, in Fig. 26, the curve A represents roughly the mechanical
power equivalent of light for average intensity, that is, the power
required to produce the same physiological effect or the same
candle power, the distribution of power in an incandescent lamp
YELLOW GREEN
FIG. 26.
carbon filament would be somewhat like C. That is, the physio-
logical effect falls off somewhat towards the green, as C drops
more than A, and almost vanishes in the blue and violet, as C
rapidly decreases, while A, the power required to give the same
physiological effect, rapidly increases. From the yellow towards
the red the physiological effect again decreases somewhat, but
50 RADIATION, LIGHT, AND ILLUMINATION.
the radiation still increases towards the ultra-red. Dividing C
by A then gives the distribution of the physiological effect, curve
C', that is, of visibility, in the incandescent lamp spectrum, show-
ing that the color of the light is yellow. Hg gives the distribu-
tion of power in the mercury spectrum. It is shown in dotted
lines, as the distribution is not continuous, but the power massed
at definite points, the spectrum lines of mercury. Hg' then gives
the visibility curve by dividing Hg by A. As seen, the ratio of
the area of Hg* to Hg, that is, the ratio of the physiological effect
to the power, is much less than the ratio of the area of C' to C;
that is, the former produces for the same amount of visibility far
less heat and thus is safer.
25. Excessive intensity, such as produced at a short-circuiting
arc, is harmful to the eye. The human organism has by evolu-
tion, by natural selection, developed a protective mechanism
against the entrance of radiation of excessive power into the eye :
at high intensity of illumination the pupil of the eye contracts
and thus reduces the amount of light admitted, and a sudden
exposure to excessive radiation causes the eyelids to close. This
protective mechanism is automatic; it is, however, responsive
mainly to long waves of radiation, to the red and the yellow light,
but not to the short waves of green, blue and violet light. The
reason for this is apparently that all sources of excessive radia-
tion which are found in nature, the sun and the fire, are rich in
red and yellow rays, but frequently poor in rays of short wave
length, and, therefore, a response to short wave lengths alone would
not be sufficient for protection as they might be absent in many
intense radiations, while a response to long waves would be
sufficient since these are always plentiful in the intense radiations
found in nature.
It is only of late years that illuminants, as the mercury lamp,
which are deficient in the long waves, have been produced, and for
these the protective action of the eye, by contracting the pupil,
fails. This absence or reduction of the contraction of the pupil
of the eye in the light of the mercury lamp is noticed when passing
from a room well illuminated by incandescent lamps, to one equally
well illuminated by mercury lamps and inversely. When changing
from the incandescent light to the mercury light, the illumination
given by the latter at first appears dull and inferior as the pupil
is still contracted, but gradually gains in intensity as the pupil
PHYSIOLOGICAL EFFECTS OF RADIATION. 51
opens; and inversely, coming from the mercury light to the incan-
descent light, the latter first appears as a big glare of light, the
pupil still being open, but gradually dulls down by the contraction
of the pupil.
This absence of the automatic protective action of the eye
against light deficient in long waves is very important, as it means
that exposure to excessive intensity of illumination by mercury
light may be harmful, due to the power of the light, against which
the eye fails to protect, while the same or even greater power of
radiation in yellow light would be harmless, as the eye will pro-
tect itself against it. The mercury lamp, therefore, is the safest
illuminant, when of that moderate intensity required for good
illumination, but becomes harmful when of excessive intensity, as
when closely looking at the lamp for considerable time, when
operating at excessive current. The possibility of a harmful
effect is noticed by the light appearing as glaring. This phe-
nomenon explains the contradictory statements occasionally made
regarding the physiological effect of such illuminants.
26. Up to and including the green light, no specific effects,
that is, effects besides those due to the power of radiation, seem
yet to exist. They begin, however, at the wave length of blue
light.
I show you here a fairly intense blue violet light, that is, light
containing only blue and violet radiation. It is derived from a
vertical mercury lamp, which is surrounded by two concentric
glass cylinders welded together at the bottom. The space be-
tween the cylinders is filled with a fairly concentrated solution
of potassium permanganate (strong copper nitrate solution or a
cupric-ammon salt solution, though not quite so good may also
be used) which is opaque to all but the blue and violet radiations.
As you see, the light has a very weird and uncanny effect, is
extremely irritating: you can see by it as the intensity of illumi-
nation is fairly high, but you cannot distinguish everything, and
especially the lamp is indefinite and hazy : you see it, but when
you look at it it disappears, and thus your eye is constantly try-
ing to look at it and still never succeeds, which produces an
irritating restlessness. It can well be believed that long exposure
to such illumination would result in insanity. The cause of this
weird effect — which is difficult to describe — is that the sensitive
spot on the retina, that is, the point on which we focus the image
52 RADIATION, LIGHT, AND ILLUMINATION.
of the object which we desire to see, or the fova F in Fig. 19, is
blue blind, that is, does not see the blue or violet light. Thus we
see the lamp and other objects indistinctly on the outer range of
the retina, but what we try to see distinctly disappears when
focused on the blue blind spot F. This spot, therefore, is often
called the " yellow spot," as we see yellow on it — due to the
absence of the vision of blue at this particular place of the retina.
To produce this effect requires the mercury lamp; most other
illuminants do not have sufficient blue and violet rays to give
considerable illumination of this color and even if they do, no
screen which passes blue and violet is sufficiently opaque to the
long waves not to pass enough of them to spoil the effect, if the
illuminant is rich in such long waves. The mercury lamp, how-
ever, is deficient in these, and thus it is necessary only to blind off
the green and yellow rays in order to get the blue and violet light.
I show you here a mercury lamp enclosed by a screen consist-
ing of a solution of naphtol green (an aniline dye) which transmits
only the green light. As you see, in the green the above-described
effect does not exist, but the vision is clear, distinct and restful.
27. Beyond the violet the radiation is no longer visible to the
eye as light. There is, however, a faint perception of ultra-violet
light in the eye, not as distinct light, but rather as an indis-
tinct, uncomfortable feeling, some form of dull pain, possibly
resulting from fluorescence effects caused by the ultra-violet
radiation inside of the eye. With some practice the presence of
ultra-violet radiation thus can be noticed by the eye and such
light avoided. In the ultra-violet, and possibly to a very slight
extent in the violet and even in the blue, a specific harmful effect
appears, which probably is of chemical nature, a destruction by
chemical dissociation. This effect increases in severity the
further we reach into the ultra-violet, and probably becomes a
maximum in the range from one to two octaves beyond the violet.
These very short ultra-violet rays are extremely destructive to
the eye : exposure even to a moderate intensity of them for very
few minutes produces a severe and painful inflammation, the
after effects of which last for years, and long exposures would
probably result in blindness. The chronic effects of this inflam-
mation are similar to the effect observed in blue light : inability
or difficulty in fixing objects on the sensitive spot F, so that with-
out impairment of the vision on the rest of the retina clear dis-
PHYSIOLOGICAL EFFECTS OF RADIATION. 53
tinction is impaired and reading becomes difficult or impossible,
especially in artificial illumination. It appears as if the sensitive
spot F, or the focusing mechanism of the eye, were over-irritated
and when used, for instance in reading, becomes very rapidly
fatigued and the vision begins to blur. If further irritation by
ultra-violet light or by attempting to read, etc., is avoided,
gradually the rapidity of fatigue decreases, the vision remains
distinct for a longer and longer time before it begins to blur and
ultimately becomes normal again.
The inflammation of the eye produced by ultra-violet light
appears to be different from that caused by exposure to high-
power radiation of no specific effect, as the light of a short circuit
of a high-power electric system, or an explosion, etc.
The main differences are:
1. The effect of high-power radiation (power burn) appears
immediately after exposure, while that of ultra-violet radiation
(ultra-violet burn) appears from 6 to 18 hours after exposure.
2. The external symptoms of inflammation: redness of the
eyes and the face, swelling, copious tears, etc., are pronounced
in the power burn, but very moderate or even entirely absent
in the ultra-violet burn.
3. Complete recovery from a power burn even in severe cases
usually occurs within a few days, leaving no after effects, while
recovery from an ultra-violet burn is extremely slow, taking
months or years, and some after effects, as abnormal sensitivity
to radiation of short wave lengths, may be practically permanent.
The general phenomena of a severe power burn are :
Temporary blindness immediately after exposure, severe pains
in the eyes and the face, redness of eyes and face, swelling, copi-
ous tears, etc. These effects increase for a few hours and then
decrease, yielding readily to proper treatment: application of
ice, cold boric acid solution, etc., and complete recovery occurs
within a few days.
In chronic cases, as excessive work under artificial illumination,
the symptoms appear gradually, but recovery, if no structural
changes in the eyes have occurred, is rapid and complete by
proper treatment and discontinuance of work under artificial
illumination.
Most artificial light is given by temperature radiation (incan-
descent lamp, gas and kerosene flame), and therefore its radiation
54 RADIATION, LIGHT, AND ILLUMINATION.
consists of a very small percentage only of visible light (usually
less than 1 per cent), while most of its energy is in the ultra-red
and invisible, and for the same amount of visible radiation or
light the total radiated power thus is many times greater than
with daylight. Regarding chronic " power burn," artificial light,
therefore, is much more harmful than daylight, that is, much
more energy enters the eye under incandescent illumination than
under much more powerful daylight illumination.
In a severe ultra-violet burn no immediate symptoms are
noticeable, except that the light may appear uncomfortable
while looking at it. The onset of the symptoms is from 6 to 18
hours later, that is, usually during the night following the ex-
posure, by severe deep-seated pains in the eyes; the external
appearance of inflammation is moderate or absent, the vision is
not impaired, but distinction made difficult by the inability to
focus the eye on any object. The pains in the eyes and head-
ache yield very slowly; for weeks and even months any attempt
of the patient to use the eyes for reading, or otherwise sharply
distinguishing objects, leads to blurring of the vision; the letters
of the print seem to run around and the eye cannot hold on
to them, and severe headache and deep-seated pains in the
eyes follow such attempt. Gradually these effects become less;
after some months reading for a moderate length of time during
daylight is possible, but when continued too long, or in poor
light, as in artificial illumination, leads to blurring of the vision
and head or eye ache. Practically complete recovery occurs
only after some years, and even then some care is necessary, as
any very severe and extended strain on the eyes temporarily
brings back the symptoms. Especially is this the case when
looking at a light of short wave length, as the mercury arc; that
is, there remains an abnormal sensitivity of the eye to light of
short wave lengths, even such light which to the normal eye is
perfectly harmless, as the mercury lamp.
In chronic cases of ultra-violet burn, which may occur when
working on unprotected arcs, and especially spark discharges
(as in wireless telegraphy), the first symptoms are: occasional
headaches, located back of the eyes, that is, pains which may
be characterized either as headache or as deep-seated eye ache.
These recur with increasing frequency and severity. At the
same time the blurring of the vision begins to be noticeable
PHYSIOLOGICAL EFFECTS OF RADIATION. 55
and the patient finds it more and more difficult to keep the eye
focused for any length of time on objects, as the print when read-
ing. These symptoms increase m severity until the patient
is obliged to give up the occupation which exposed him to ultra-
violet light, and then gradual recovery occurs, as described above,
if the damage has not progressed too far.
In mild cases recovery from power burns may occur in a few
hours and complete recovery from mild ultra-violet burns in
a few weeks.
Both types of burn may occasionally occur simultaneously
and their symptoms then successively.
For instance, in a case of an exposure while working for about
half an hour with a flame-carbon arc without enclosing glass
globe (such an arc contains large amounts of high-power radia-
tion, of yellow and orange color, but also a considerable amount
of ultra-violet rays), the symptoms of the power burn increased
in severity for a few hours, and then rapidly vanished by the
application of cold water, and recovery was practically complete
six hours after exposure; then some hours later, in the middle
of the night, the patient was awakened by severe pains in the
eyes, the symptoms of the ultra-violet burn, and had to seek
medical attendance. Under proper treatment recovery occurred
in a few days, but the blurring of the vision was appreciable
for some days longer, and the sensitivity to high-frequency light
for some weeks.
28. Arcs produce considerable amount of ultra-violet light,*
and in former experiments we have used a high frequency iron
arc for producing ultra-violet light and also have seen that even a
very thin sheet of glass is opaque for these radiations. For very
long ultra-violet rays, that is, the range close to the visible violet,
glass is not quite opaque, but becomes perfectly opaque for about
one-quarter to one-half octave beyond the violet, and in this first
quarter of an octave the harmful effect of the ultra-violet radia-
tion is still very small and becomes serious only when approach-
ing a distance of about one octave from the visible end of the
violet. Clear transparent glass thus offers a practically complete
protection against the harmful effects of ultra-violet light, except
when the latter is of excessive intensity, and thus arcs enclosed
* An arc between silicon terminals emits especially powerful ultra-violet
radiation accompanied by little visible light.
56 RADIATION, LIGHT, AND ILLUMINATION.
by glass globes are harmless. It is, however, not safe to look
into and work in the light of open metal arcs for too long a
time.
The carbon arc gives the least ultra-violet rays, so little that
even without enclosure by glass it is fairly safe; metal arcs give
more and the mercury arc gives the greatest amount and reaches
to the farthest distance beyond the visible, and these very destruc-
tive very short ultra-violet rays have so far only been observed in
the radiation of a low temperature mercury arc in a quartz tube :
quartz being transparent to these rays while glass is opaque.
The high temperature mercury arc in a quartz tube, that is, arc
operated near atmospheric pressure as it is used to some extent
for illumination, especially abroad, seems to be much less dan-
gerous than the low temperature or vacuum arc, but it also
requires a protecting glass globe.
In general, no metal arc, spark discharge, or glow discharge
should ever be used industrially or otherwise without being en-
closed by a glass globe, preferably of lead glass, if located so that
it may be looked at. Those experimenting with arcs or other
electric discharges should always protect their eyes by the inter-
position of a glass plate.
Thus the sparks of wireless telegraph stations, the discharges
of ozonizers, the arcs of nitric acid generators, electric furnaces,
etc., may be dangerous without glass enclosure.
While artificial illuminants, and especially metal arcs, give
an appreciable amount of ultra-violet light, these ultra-violet
rays extend only to about one-quarter octave beyond the visible
violet and if, as is always the case, the illuminant is enclosed by
glass, the harmful effect of these long ultra-violet rays is negli-
gible. The radiation of the sun also contains ultra-violet rays,
and a larger percentage compared with the total radiation than
any glass-enclosed artificial illuminant, and as the light of the sun,
that is, daylight, is recognized as perfectly harmless, as far as
this specific destructive action is concerned, the same applies to
the artificial illuminants, as they contain less ultra-violet rays
than the light of the sun.
This specific destructive action on the eye of short ultra-violet
radiation extends beyond the blank space in the spectrum of
radiation (Fig. 14) and still exists, though possibly to a lesser
extent, in the X-rays.
PHYSIOLOGICAL EFFECTS OF RADIATION. 57
Pathological and Therapeutic Effects of Radiation.
29. Radiation impinging on the tissue of the human body
or other living organisms exerts an influence depending on
intensity, power and frequency. The effect on the eye has been
discussed in the preceding paragraphs. The specific chemical
effect in supplying the energy of plant life will be more fully
discussed in the following under chemical effects. As is to be
expected, the effect of radiation on the living protoplasm
of the cells is stimulating if of moderate intensity, destructive
if of excessive intensity; that is, by the energy of the radiation
the motions of the parts of the protoplasm-molecule are in-
creased, and, if the intensity of radiation is too high, the mole-
cule thus is torn asunder, that is, destroyed, the living cell
killed and inflammation and necrosis (mortification) result.
If the intensity is moderate, merely an increase of the rapidity
of the chemical changes in the protoplasm, which we call life,
results; that is, the radiation exerts a stimulating effect, in-
creasing the intensity of life, causing an increased renewal of
worn-out tissue and reconstruction, and thus is beneficial or
curative, especially where the metabolism is sluggish.
Just as in the action on the eye, two different effects probably
exist : a general effect due to the energy of the radiation — which
with sunlight is a maximum beyond the visible close to the red
end of the spectrum, and with most artificial illuminants (those
based on incandescence) reaches a maximum still further in
the ultra-red — and a specific effect depending on the frequency.
The power effect is general and probably fairly uniform
throughout the exposed tissue, appears simultaneous with or
immediately after the exposure, and thus practically no danger
of harmful results from destruction of tissue exists, as excessive
intensity makes itself felt immediately, before far-going destruc-
tion of tissue can occur, and, therefore, the only possible danger
which could exist would be in the indirect effect of stimulation
on other organs of the body, as the heart. Thus the use of in-
candescent light as stimulant appears fairly harmless.
Different is the specific action of high-frequency radiation.
This occurs only some time after exposure, from a few hours to
several weeks (with X-rays) . As these higher frequencies are not
felt by the body as such and exert a powerful action even at such
58 RADIATION, LIGHT, AND ILLUMINATION.
low intensities that their energy is not felt as heat, and, further-
more, . the susceptibility of different people may be different,
there is nothing to guard against excessive and thereby harmful
exposure. Furthermore, the damage is far more severe and
lasting than with the power effect, and fatal cases have occurred
years after exposure. Possibly, as may be expected from
selective action, only a few cells in the living tissue are killed
by the radiation, and the disintegration products of these dead
cells then gradually involve the surrounding living cells, causing
their destruction or degeneration, so that the harm is far out of
proportion with the immediate destructive effect of the radia-
tion proper, especially with penetrating forms of radiation, as
X-rays and radium rays, in which the lesions are correspondingly
deep-seated.
High-frequency radiation (violet, ultra-violet, X-ray) should
therefore be used only under the direction of experts fully
familiar with their physiological action and danger.
The specific action of high-frequency radiation is still absent
in the green, begins slightly in the blue and violet, increases
into the ultra-violet and persists up to the highest frequencies of
the X-rays. It is shared also by the radiation of the radio-active
substances, as the alpha and beta rays of radium. While the
maximum of this effect probably also lies in the ultra-violet,
from one to two octaves beyond the visible spectrum, the
effect is profoundly modified by the transparency or opacity of
the tissue for different frequencies, and the character of the stimu-
lating and pathological effects greatly depends on the depth to
which the radiation penetrates the body.
The largest part of the organism is water. Water is trans-
parent for visible light, becomes more and more opaque in the
ultra-red as well as in the ultra-violet, and is again fairly trans-
parent for X-rays. Blood is fairly transparent for the long
visible rays of red and yellow, but nearly opaque for the shorter
violet and ultra-violet rays. Hence next to the X-rays which
can pass through the body, the longest visible rays of red and
yellow penetrate relatively deepest into the body, though even
they are practically absorbed within a short distance from the
surface. Thus while the energy maximum of the sunlight
is in the ultra-red, the maximum physiological effect probably
is that of the red and yellow rays : the same which are the active
PHYSIOLOGICAL EFFECTS OF RADIATION. 59
rays in plant life. The violet and ultra-violet rays are absorbed
close to the surface of the body by the blood, which is opaque
for them. They can thus be made to penetrate deeper — as is
done in their therapeutic use — by freeing the tissue of the body
from blood by compression or other means. Even then, how-
ever, probably only the longest ultra-violet rays penetrate, the
very short ones being kept out by the opaque character of the
water in the tissue.
The penetration of the radiation of the sunlight into the human
body is very greatly reduced by acclimatization, which leads
to the formation of a protective layer or pigment, more or less
opaque to the light. Such acclimatization may be permanent
or temporary. Permanent acclimatization has been evolved
during ages by those races which developed in tropical regions,
as the negroes. They are protected by a black pigment under
the skin, and thereby can stand intensities of solar radiation
which would be fatal to white men. A temporary acclimatiza-
tion results from intermittent exposure to sunlight for gradually
increasing periods : tanning, and enables the protected to stand
without harmful effects exposure to sunlight which would pro-
duce severe sunburn in the unprotected. This acquired protec-
tion mostly wears off in a few weeks, but some traces remain
even after years.
A slight protection by pigmentation also exists in white men,
and its differences lead to the observed great differences in sensi-
tivity to solar radiation: blondes, who usually have very light
pigmentation, are more susceptible to sunburn and sunstroke than
the more highly pigmented brunette people.
In sunburn we probably have two separate effects super-
imposed upon the other: that due to the energy of the solar
radiation and the specific effect of the high frequencies, which
to a small extent are contained in the sunlight. The two effects
are probably somewhat different, and the high-frequency effect
tends more to cause inflammation of the tissue, while the energy
effect tends towards the production of pigmentation (tanning),
and the symptoms of sunburn thus vary with the different pro-
portions of energy radiation and of high-frequency radiation as
depending on altitude, humidity of the air, the season, etc.
30. The action of radiation on living organisms is stimulating
if of moderate intensity, destructive if of high intensity. Thus
60 RADIATION, LIGHT, AND ILLUMINATION.
it is analogous with that of any other powerful agent or drug,
as alcohol, caffeine, etc. The intensity of light which is destruc-
tive to life largely depends on the amount of light to which the
organism is accustomed. Those organisms which live in the
dark may be killed by an amount of light which is necessary
for the life of other organisms. Amongst the saprophytic bacilli,
for instance (the germs of putrefaction), many species live in the
light, and die, or at least do not multiply, if brought into the
dark, while other putrefactive bacilli live in the dark and are
killed by light. The latter also is the case with the pathogenic
bacilli, that is, the disease germs, as the bacillus of tuberculosis,
cholera, etc. As these live in the dark, the interior of the body,
they are rapidly killed by light. Light, and radiation in general,
therefore is one of the most powerful germicides and disinfect-
ants. One of the most effective prophylactic measures, espe-
cially against the diseases of civilization, as tuberculosis, etc., thus
is to flood our homes with light, especially direct sunlight, while
our habit of keeping the light out of our houses by curtains,
shades, etc., closing our residences almost light-tight, when
leaving them for some time, converts them into breeding places
of disease germs, and then we wonder about mortality.
Obviously excessive light intensity ultimately becomes harm-
ful even to the human organism, and it is therefore advisable
to protect ourselves against the light when it becomes annoying
by its intensity. It has even been claimed that the impossibility
of white men to become permanently acclimatized in the tropics
and the change in the temperament of the population of our
country within a few generations from their immigration:
the increased nervousness, restlessness and "strenuousness,"
are the result of the greater intensity of the sunlight, especially
its high-frequency radiation, compared with the more cloudy
climate of our original European home. Whether this is the
case remains to be further investigated. It is hard to believe,
however, that such a profound effect should result from the
exposure of a small part of the body, face and hands, to a more
intense light, and the failure of acclimatization in the tropics
could well be explained by the higher temperature and its damag-
ing effect, while the change from Europe to America is not merely
a change from a more cloudy to a more sunny climate, but
from a maritime climate, that is, climate having fairly uniform
PHYSIOLOGICAL EFFECTS OF RADIATION. 61
and slowly changing temperatures, to a continental climate,
with its rapid changes of temperature and enormous temperature
extremes, and the difference between continental and maritime
climate may be suspected as the cause in the change of the tem-
perament of the races.
As men have lived for ages in the light, the cells of the human
body are far more resisting to the light than the disease germs,
which for ages have lived in the dark; and light, and more
particularly the high-frequency violet and ultra-violet radiation
and the X-rays, thus have found a useful therapeutic application
in killing disease germs in the human body. Thus, by expos-
ing the diseased tissue to high-frequency radiation, the disease
germs are killed, or so far damaged that the body can destroy
them, while the cells of the body are still unharmed, but stimu-
lated to greater activity in combating the disease germs. As
seen, for this purpose the radiation must be of sufficient intensity
and duration to kill or damage the bacilli, but not so intense
as to harm the cells of the body. Surface infections, as tubercu-
losis of the skin (scrofulosis, lupus), thus are effectively and
rapidly cured by high-frequency light. More difficult and less
certain the effect is if the infection is deeper seated, as then
the radiation must penetrate a greater thickness of tissue to
reach the bacilli, and is thereby largely absorbed, and the danger
thus exists that, before a sufficient intensity of radiation can be
brought to the seat of the infection, the intensity at the surface
of the tissue may become harmful to the cells of the body. In
this case the more penetrating X-rays would be more applicable,
as they can penetrate to any depth into the body. They are,
however, so far distant in frequency from the light radiation,
that the acclimatization of the body to the light radiation
probably exists only to a lesser extent against the X-rays; that
is, the difference in the destructive effect on the bacilli and on
the cells of the body, on which the curative effect is based, prob-
ably is less with the X-rays than with the long ultra-violet waves.
Since Dr. Finsen introduced phototherapy and radiotherapy,
about fifteen years ago, it thus has found a very extended and
useful field, within its limitation.
This greater destructive action of radiation on micro-organisms
than on the cells of the human body, extends not merely to the
pathogenic bacilli, but to all organisms living in the dark.
62 RADIATION, LIGHT, AND ILLUMINATION.
Thus the spermatozoa — which biologically are independent
living organisms — seem to be killed by X-rays before any
damage is done to the body, and permanent sterility then
results. Amongst the cells of the body differences seem to exist
in their resistivity. It is claimed, for instance, that the sensory-
nerves are first paralyzed by violet radiation and that intense
violet light can thus be used to produce local anaesthesia, suf-
ficient for minor operations.
Occasionally the effect of light may be harmful in the relation
of the human body to invading bacilli. In some eruptive in-
fections, as smallpox, ulceration of the skin (leading to mark-
ing) seems to be avoided if the patient is kept from the light,
and the course of the disease mitigated. As red light, however,
seems to have no effect, instead of perfect exclusion of light,
which is not very feasible, the use of red light thus seems to offer
an essential advantage.
LECTURE IV.
CHEMICAL AND PHYSICAL EFFECTS OF RADIATION.
Chemical Effects.
31. Where intense radiation is intercepted by a body chemical
action may result by the heat energy into which the radiation is
converted. This, however, is not a direct chemical effect of
radiation but an indirect effect, resulting from the energy of the
radiation.
Direct chemical effects of radiation are frequent. It is such an
effect on which photography is based : the dissociating action of
radiation on silver salts, the chloride in ordinary photographic
paper, the bromide and iodide in the negative plate and the quick
printing papers. This chemical action is greatest in the violet
and ultra-violet and decreases with increasing wave length,
hence is less in the green, small in the yellow, and almost absent in
the red and ultra-red, so that the short waves, blue, violet and
ultra-violet, have sometimes been called " chemical rays." This,
however, is a misnomer, just as the term "heat rays" sometimes
applied to red and ultra-red rays. In so far as when intercepted
they are converted into heat, all rays are heat rays, but neither
the ultra-red nor any other radiation is heat, but it may become
heat when it ceases to be radiation. Thus all radiations are
chemical rays, that is, produce chemical action, if they strike a
body which is responsive to them.
The chemical action of radiation is specific to its frequency and
seems to be some kind of a resonance effect. We may picture to
ourselves that the frequency of vibration of a silver atom is that
of violet or ultra-violet light, and therefore, when struck by a
wave of this frequency, is set in vibration by resonance, just as a
tuning fork is set in vibration by a sound wave of the frequency
with which it can vibrate, and if the vibration of the silver atom,
in response to the frequency of radiation, becomes sufficiently
intense, it breaks away from the atom with which it is chemically
64 RADIATION, LIGHT, AND ILLUMINATION.
combined in the compound, the silver bromide, etc., and this
compound thus splits up, dissociates. The phenomenon, how-
ever, must be more complex, as a simple resonance vibration
would be especially pronounced at one definite frequency, the
frequency of complete resonance, and rapidly decrease for higher
and for lower frequencies. The chemical action of radiation on
silver compounds, however, does not show such a response to any
definite frequency, but, while strongest in the ultra-violet, ex-
tends over the entire range from the frequency of green light
beyond the ultra-violet and up to the highest frequencies of
X-rays. That the chemical activity of radiation is some form of
resonance, is, however, made very probable by the relation which
exists between the active frequency range and the weight of the
atom or molecule which responds to the radiation. Thus, while
the fairly heavy silver atom (atomic weight 108) responds to
rays near the violet end of the visible spectrum, the much lighter
oxygen atom (atomic weight 16) responds only to much higher
frequencies, to those of the physiologically most destructive rays,
about one to two octaves beyond the visible spectrum. These
very short radiations energetically produce ozone 03,from oxygen
02, probably by dissociating oxygen molecules 02,into free atoms,
and these free atoms then join existing molecules: 0 + 02 = 03,
thus forming ozone. Possibly their destructive physiological
action is due to this ability to cause resonance with the oxygen
atom and thereby destroy molecular structures.
32. Response to the long waves of red and ultra-red light thus
may be expected from atoms or groups of atoms which are very
much heavier than the silver atom, and this indeed seems to be
the case in the action of radiation on the life of the plants. There
the response is not by atoms, but by the much heavier groups of
atoms, radicals of carbon compounds, which separate and recom-
bine in response to radiations and thus produce in vegetable
organisms the metabolism which we call life.
The action of radiation on plant life thus seems to be a chemi-
cal action, and this would be the most important chemical action,
as on it depends the life of the vegetation and thereby also the
existence of animal life and, thus, our own. This action by which
the vegetation converts the energy of radiation into chemical
energy is related to the presence of chlorophyl, a green body
which exhibits a red fluorescence. I show you here a solution
CHEMICAL AND PHYSICAL EFFECTS OF RADIATION. 65
thereof in alcohol. This use of the energy of radiation occurs
only in those parts of the plant in which chlorophyl is present,
usually shown by its green color, that is, in the leaves and young
stems. In those plants in which the leaves have lost their chloro-
phyl in taking up other functions — as the function of protection
against attack by conversion into spines in the cacti — the stems
and trunks have acquired the function of energy supply from
radiation, and show the green color of chlorophyl. When the
leaves die in the fall their chlorophyl disappears and they change
to yellow or red color. Those parts of the plants which contain
chlorophyl, mainly the leaves, take carbon dioxide (C02) from
the air through breathing openings (stomata), absorb the radia-
tion, and convert its energy into chemical energy, and use this
energy in splitting up or dissociating the C02, exhausting the
oxygen 02 and using the carbon in producing the complex carbon
compounds of their structure: fiber (cellulose), starch, proto-
plasm, etc. The energy of plant life thus is derived from radia-
tion and their work is constructive or synthetic, that is, they
produce complex chemical compounds from simple ones: the
carbon dioxide of the air, the nitrates and phosphates of the soil,
etc. Inversely, the animal organism is analytic, it converts the
chemical energy of complex compounds into mechanical and
heat energy by splitting them into simpler compounds, burning
them in the lungs or gills. For the supply of mechanical energy
which maintains the life, the animal organism thus depends upon
the synthetic work of the vegetation by consuming as food the
complex compounds constructed by the plants from the energy
of radiation, either directly (vegetarians), or indirectly, by eating
other animals, which in their turn live on the vegetation. Thus,
while the plants take in from the air carbon dioxide C02, exhaust
the oxygen 02, and convert the C into complex compounds, the
animal takes in oxygen 02, by it burns up the complex carbon
compounds derived from the plants, and exhausts C02 as product
of combustion, but in its ultimate result, all life on the earth de-
pends for its energy on radiation, which is made available in the
plants by conversion to chemical energy and used as such by the
animals.
The radiations which supply the energy of plant life, probably
are the long waves of yellow, red and ultra-red light, while the
short waves of blue, violet and ultra-violet cannot be used by the
66 RADIATION, LIGHT, AND ILLUMINATION.
plant, but are harmful, kill the vegetation. This can easily be
understood : to the long waves of red and yellow light the atoms
do not respond, but only the much heavier groups of atoms or car-
bon radicals, and these thus separate and recombine and thereby
constitute what we call life. To very short waves, that is, high
frequencies, these heavy groups of atoms cannot respond, but
single atoms would respond thereto and thus by their separation
break up and destroy the atomic groups. That is, the resonant
dissociation produced by low frequency of radiation extends only
to the groups of atoms and thereby results in their separation and
recombination to heavier molecules : life, while the resonant dis-
sociation produced by high frequencies extends to the atom and
thereby splits up and destroys the molecules of the living organ-
ism, that is, death. Therefore the short waves of radiation,
green, blue, etc., which are more or less harmful to plants, are
not used but are reflected by the chlorophyl; hence the green
color. To some extent violet radiation is absorbed by chloro-
phyl, but it is questionable whether the energy of violet light
directly contributes to the chemical action, and it is rather
probable that the violet radiation is converted into red light by
fluorescence — chlorophyl fluoresces red — and used as red
light. Excessive violet radiation seems to be harmful.
Physical Effects.
33. Some of the most interesting physical effects of radiation
are those by which it is converted into another form of radiation :
fluorescence and phosphorescence.
Many substances have the property of converting some of the
radiation which is absorbed by them into radiation of a different
wave length, that is, act as frequency converter of radiation,
fluorescence. Many bodies when exposed to radiation store some
of the energy of radiation in such a manner as to give it out again
afterwards and thus, after exposure to light, glow in the darkness
with gradually decreasing intensity, phosphorescence. These
phenomena probably belong to the least understood effects
of radiation. They are very common, but phosphorescence
usually lasts such a short time that it can be observed only
by special apparatus, although a few bodies continue to phos-
phoresce for hours and even days. Fluorescence also is usually
CHEMICAL AND PHYSICAL EFFECTS OF RADIATION. 67
so weak as to escape notice, although in a few bodies it is very
strong.
The change of frequency in fluorescence always seems to be a
lowering of the frequency, that is, an increase of wave length, and
in phosphorescence also the light given out seems always to be
of lower frequency than the light absorbed and indeed, fluores-
cence and phosphorescence seem to be essentially the same
phenomenon, radiation is absorbed and its energy given out again
as radiation of lower frequency and that part of the returned
radiation which appears during the absorption we call fluores-
cence, that part which appears later, phosphorescence. There is,
however, frequently a change of the color of the light between
fluorescence and phosphorescence and also between phosphores-
cence immediately after exposure to light and some time after-
wards. For instance, some calcite (calcium carbonate or lime-
stone) fluoresces crimson, but phosphoresces dark red. The
phosphorescence of calcium sulphide changes from blue in the
beginning to nearly white some time after, etc.
Due to the change of frequency to longer waves the longest
visible rays, red, orange and yellow, produce no fluorescence or
very little thereof, as their fluorescent and phosphorescent radia-
tion would usually be beyond the red, in the invisible ultra-red.
Blue, violet and ultra-violet light produce the most intense
effects, as a lowering in frequency of these radiations brings them
well within the visible range.
Ultra-violet light is best suited for studying fluorescence as it is
not visible, and thus only the fluorescent light is visible; white
light, for instance, does not show the same marked effect, since the
direct white light is superimposed upon the light of fluorescence.
Most brilliant effects, however, are produced by using a source of
light which is deficient in the frequencies given by fluorescence
and then looking at the fluorescent body through a glass having
the same color as that given by fluorescence. Thus the least
traces of red fluorescence can be discovered by looking at the
body through a red glass, in the illumination given by the mer-
cury lamp. As the mercury lamp contains practically no red
rays, seen through a red glass everything appears nearly black or
invisible except red fluorescent bodies, which appear self-lumi-
nous, glowing in a light of their own, and appear like red hot
bodies.
68 RADIATION, LIGHT, AND ILLUMINATION.
In the illumination given by the mercury lamp I here drop a
few drops of a solution of rhodamine 6 G, rhodamine R and
uranine (aniline dyes) into a large beaker of water. As you see,
when sinking down and gradually spreading, they appear —
especially against a dark background — as brilliant luminous
clouds of orange, red and green, and seen through a red glass
they appear like clouds of fire. I change to the illumination
given by the incandescent lamp and all the brilliancy disappears,
fluorescence ceases and we have a dull red colored solution. I
show you here the sample card of a silk store of different colored
silks. Looking at it through a red glass, in the mercury light all
disappear except a few, which you can pick out by their lumi-
nosity: they are different colors, pinks, reds, heliotrope, etc., but
all containing the same red fluorescent aniline dye, rhodamine.
A glass plate coated with a thick layer of transparent varnish,
colored by rhodamine, appears like a sheet of red hot iron in the
mercury light, especially through a red glass, while in the light of
the incandescent lamp it loses all its brilliancy.
This solution of rhodamine 6 G in alcohol, fluoresces a glaring
orange in the mercury light, in the light of a carbon arc lamp (or
in daylight) it fluoresces green and less brilliant. Thus you see
that the color of the fluorescent light is not always the same, but
depends to some extent on the frequency of radiation which
causes the fluorescence.
Here I have a sheet of paper covered with calcium sulphide
and a lump of willemite (zinc silicate) and some pieces of calcite.
As you see, none of them show any appreciable fluorescence
in the mercury light. But if I turn off the mercury light, the
calcium sulphide phosphoresces brightly in a blue glow, the others
do not. Now I show you all three under the ultra-violet rays of
the condenser discharge between iron terminals, or ultra-violet
lamp (Fig. 11) and you see all three fluoresce brilliantly, in blue,
green and red. Turning off the light all three continue to glow
with about the same color, that is, phosphoresce, but the red
fluorescence of the calcite very rapidly decreases, the green glow
of the willemite a little slower, but the blue glow of the calcium
sulphide screen persists, decreasing very little. I now hold my
hand back of it and close to it and you see the picture of the hand
appear on the screen by an increase of the luminosity where by
contact with the hand the temperature of the screen was slightly
CHEMICAL AND PHYSICAL EFFECTS OF RADIATION. 69
raised, thus showing the effect of the temperature rise in increas-
ing phosphorescence.
These substances which I show you, calcium sulphide, cal-
cium carbonate (calcite), zinc silicate (willemite), are not fluo-
rescent or phosphorescent themselves, but their luminescence is
due to a small percentage of some impurities contained in them.
Chemically pure substances and concentrated solutions of the
aniline dyes, or these dyes in their solid form, do not show the
luminescence, but only when in very diluted solutions; that is,
luminescence as fluorescence and phosphorescence seems to be
the property of very diluted solutions of some substances in
others. Thus a sheet of paper or cardboard colored red by
rhodamine does not fluoresce, but if a small quantity of rhoda-
mine is added to some transparent varnish and the paper colored
red by a heavy layer of this varnish it fluoresces brightly red.
To show you the fluorescent spectrum, I have here a mercury
lamp surrounded by a very diluted solution of rhodamine 6 G,
and some rhodamine R, contained between two concentric glass
cylinders. As you see, through the spectroscope a broad band
appears in the red and the green light has faded considerably.
You also notice that the light of this lamp, while still different
from white light, does not give anything like the ghastly effect of
human faces, as the plain mercury lamp, but contains considerable
red rays, though not yet enough. I also show you a mercury
lamp surrounded by a screen of a very dilute solution of uranine:
you see, its light is bright greenish yellow, but much less ghastly
than the plain mercury light and the spectroscope shows the
mercury lines on a fluorescent spectrum, which extends as a con-
tinuous luminous band from the green to and beyond the red.
You also see that with this uranine screen the mercury lamp
gives more light than without it : considerable of its ultra-violet
and violet light is converted to yellow and thereby made visible
or more effective.
LECTURE V.
TEMPERATURE RADIATION.
34. The most common method of producing radiation is by
impressing heat energy upon a body and thereby raising its tem-
perature. Up to a short time ago this was the only method avail-
able for the production of artificial light. The temperature is
raised by heating a body by the transformation of chemical
energy, that is, by combustion, and in later years by the trans-
formation of electric energy, as in the arc and incandescent
lamp.
With increasing temperature of a body the radiation from the
body increases. Thus, also, the power which is required to main-
tain the body at constant temperature increases with increase of
temperature. In a vacuum (as approximately in the incandes-
cent lamp) , where heat conduction and heat convection from the
radiating body is excluded, all the power input into the body is
radiated from it, and in this case the power input measures the
power of the radiation.
The total power or rate at which energy is radiated by a heated
body varies with the fourth power of its absolute temperature,
that is :
If A = surface area, Tl = absolute temperature of the radia-
tor and T2 = absolute temperature of the surrounding objects
on which the radiation impinges : the total power radiated by the
body is (Stefan's Law) :
Pr = kA (TV - ?V), (1)
where for a black body, as the carbon filament with Pr given
in watts per square cm. k is of the magnitude
k = 5 X 1(T12; (2)
!T2 is usually atmospheric temperature or about 300 degrees abs.
If Tl does not differ much from Tv that is, when considering
the radiation of a body raised slightly above the surround-
70
TEMPERATURE RADIATION. 71
ing temperature, as an electric machine, equation (1) can be
written :
Pr = kA (T, - T2) (TV + T*T2 + 7\7y + 7y);
or, approximately,
Pr = 4 kAT* (T, - T), (3)
where T is the room temperature (Tl — T) the temperature rise
of the radiator above room temperature; that is, for moderate
temperature differences the radiation power is proportional to
the temperature rise.
This equation (3) gives the law generally used for calculating
temperature rise in electric machinery and other cases where the
temperature rise is moderate. Obviously, in air the power given
off by the heated body, P, is greater than the power radiated, Pr,
due to heat convection by air currents, etc., but as heat conduc-
tion and convection also are approximately proportional to the
temperature rise, as long as the latter is moderate, equation (3)
can still be used, but with the numerical value of k increased to
k^ so as to include the heat conduction and convection: in
stationary air A^ reaches values as high as fct = 25 X 10~12 to
50 X 10~12.
As soon, however, as the temperature rise (Tl — T) becomes
comparable with the absolute temperature T, the equation (3)
can no longer be used, but the complete equation (1) must be
used, and when the temperature of the radiator, Tv is very much
greater than the surrounding temperature T2, T24 becomes negli-
gible compared with 7\4 and equation (1) can, for high tempera-
tures, thus be approximated by:
Pr = kATf; (4)
That is, the radiation power, as function of the temperature,
gradually changes from proportionality with the temperature
rise, at low temperature rise, to proportionality with the fourth
power of the temperature for high temperature rises.
Inversely then, with increasing power input into the radiator
and thus increasing radiation power, its temperature first rises
proportional to the power input and then slower and ultimately
approaches proportionality with the fourth root of the power
output: 4/p-
T =V — •
ll V kA
72
RADIATION, LIGHT, AND ILLUMINATION.
In Fig. 27 is shown the radiation curve, with the temperatures
T as ordinates and the radiated power Pr as abscissas, the upper
curve with 100 times the scale of abscissas.
Thus, to double the temperature rise from 10 deg. cent, to 20
deg. cent, requires doubling the power input. To double, how-
ever, the temperature rise from 1000 deg. cent, to 2000 deg. cent,
requires an increase of the power input from 12734 to 22734, or
more than ten fold. At high temperature the power input, there-
fore, increase enormously with the increase of temperature.
FIG. 27.
With bodies in a vacuum, the radiation power is the power
input and this above law can be used to calculate the tempera-
ture of the radiator from the power input. In air, however, a
large part of the energy is carried away by air currents, and
this part of the power does not strictly follow the temperature
law of radiation, equation (1). For radiators in stationary air
(that is, not exposed to a forced blast, as the centrifugal blast of
revolving machinery), the total power input for high tempera-
ture (as expended by radiation and heat convection) varies with
a high power of the temperature, so that the radiation law equa-
tion (1) can still be used to get a rough approximation of the
relative values of temperatures.
It, therefore, is not permissible to assume the temperature rise
as proportional to the power input as soon as the temperature
TEMPERATURE RADIATION. 73
rise is considerable and even in electrical apparatus of fire-proof
construction as some rheostats, etc., where a higher temperature
rise is permitted, the calculation of this temperature rise must be
approximated by the general law (1) and not the law of propor-
tionality (3), as the latter would 'give entirely wrong results.
For instance, assuming a temperature rise of 50 deg. cent, per
watt per sq. in. a cast silicon rod, which — at bright incandes-
cence — can dissipate 200 watts per sq. in. would give by (3), a
temperature rise of 10,000 deg. cent. This obviously is impos-
sible, as silicon melts at about 1400 deg. cent.
35. With increasing temperature of the radiator, the intensity
of the radiation increases, and at the same time the average
frequency of radiation also increases, that is, the higher frequen-
cies increase more rapidly than the lower frequencies and higher
and higher frequencies appear, until ultimately frequencies are
reached where the radiation becomes visible to the eye, as light.
When with increasing temperature the radiation just begins to be
visible, it appears as a faint colorless grey, "gespenster grau"
exhibiting the same weird and indistinct appearance as are seen
at higher intensities in the monochrome blue and violet radia-
tions ; that is, we see a faint grey light, but when we look at it, it
has disappeared : the reason is that the sensitivity of the sensitive
spot of the eye for very faint light is less than that of the surround-
ing retina and the first glimmer of light thus disappears as soon
as we focus it on the sensitive spot. With increasing tempera-
ture, first the lowest of the visible frequencies appear and become
visible as red light, and with still further increase of temperature
gradually orange, yellow, green, blue, violet and ultra-violet rays
appear and the color thus changes from red to orange, yellow,
yellowish white and then white, the latter at that temperature
where all the visible radiations are present in the same propor-
tion as in daylight. With still further increase of temperature,
the violet end of the spectrum would increase faster than the red
end and the light thus shift to bluish white, blue and violet.
The invisibility of the radiation of low temperature is not due
to low intensity. I have here an incandescent lamp at normal
brilliancy. If I decrease the power input and thereby the radi-
ated power to T^ it becomes invisible, but if we move away from
the lamp to 10 times the previous distance, we get only T^ the
radiation reaching our eyes and still the light is very plainly
74 RADIATION, LIGHT, AND ILLUMINATION.
visible. The invisibility in the former case, thus, is not due to low
intensity, but to low frequency.
The fraction of the total radiation, which is visible to the eye
as light, thus increases with the increasing temperature, from
zero at low temperature — where the radiator does not give
sufficiently high frequencies to be visible — and very low values
when it just begins to be visible in red light, to a maximum at that
temperature where the average frequency of the radiation is in
the visible range, and it would decrease again for still higher
temperature by the average frequency of radiation shifting
beyond the visible into the ultra-violet. The efficiency of light
production by incandescence thus rises with increasing tempera-
ture to a maximum, and then decreases again. As the total
radiation varies with the fourth power of the temperature, it thus
follows that the visible radiation first varies with a higher power
of the temperature than the fourth, up to the maximum efficiency
point, and beyond that increases with less than the fourth power
of the temperature. The temperature at which the maximum
efficiency of light production by incandescence occurs, that is,
where the average frequency of temperature radiation is in the
visible range, probably is between 5000 and 8000 deg. cent, and
as the most refractory body, carbon, boils at 3750 deg. cent., this
temperature thus is unattainable with any solid or liquid radiator.
Practically all bodies give the same temperature radiation,
that is, follow the temperature law (1), differing only by the
numerical value of the constant fc; that is, with increase of
temperature the radiation intensity increases and the average
frequency of radiation increases in the same manner with most
solid and liquid bodies, so that at the same temperature all the
bodies of normal temperature radiation give the same radiation
curve; that is, the same distribution of intensity as function of
the frequency and thus the same fraction of visible to total radia-
tion, that is, the same efficiency of light production.
If T is the absolute temperature in deg. cent, and lw the wave
length of radiation, the power radiated at wave length /„, and
temperature T1 by normal temperature radiation is :
b
P (IJ = c,Alw % ^ , (Wien's law) ;
or' r • i. * r1
P (U = c,Alw a\e V-l\ (Planck's law) ;
TEMPERATURE RADIATION. 75
where a = 5 for normal temperature radiation or black body
radiation; b = 1.42, and A = surface area of the radiator.
Integrating the formula of Wien's law over lw from 0 to oo ,
gives the total radiation :
P- f °°P (lw)dlw = Mr-1;
«/o
thus, for a = 5;
or, Stephan's law, as discussed above.
The maximum energy rate at temperature T occurs at the wave
length lw = lm given by:
dP (lw)
~Ji — = °>
dlw
which gives:
lmT =- = 0.284;
a
or,
0.284
= 50 X 10~6 thus gives:
T - = 5680 deg.
With normal temperature radiation the efficiency of light pro-
duction is thus merely a function of the temperature and does
not depend upon the material of the radiating body, provided
that the material is such as to withstand the temperature.
As the efficiency maximum of normal temperature radiation is
far beyond the attainable, within the range of temperature avail-
able up to the boiling point of carbon, the efficiency of light pro-
duction by incandescence continuously increases, but even then
the octave of visible radiation is at the far upper end of the radia-
tion curve, and thus the problem of efficient light production is
to operate the radiator at the highest possible temperature.
The efficiency of light production is rather low even at the
maximum efficiency point and with the average frequency of
radiation in the visible range, since this visible range is less than
one octave; under these most favorable conditions the visible
76 RADIATION, LIGHT, AND ILLUMINATION.
energy probably does not much exceed 20 per cent of the total
radiation, the rest falls below and above the visible frequencies.
36. At the highest attainable temperature, the boiling point
of carbon, the efficiency is much lower, probably below 10 per
cent and this would be the highest efficiency attainable by normal
temperature radiation. It is utilized for light production in the
carbon arc lamp. The carbon arc flame gives practically no
light, but all the light comes from the incandescent tips of the
carbon electrodes, mainly the positive, which are at the boiling
point of carbon and thus give the most efficient temperature
radiation.
Obviously, in the carbon arc lamp a very large part of the
energy is wasted by heat conduction through the carbons, heat
convection by air currents, etc., and the total efficiency of the
carbon arc lamp, that is, the ratio of the power of the visible
radiation to the total electric power input into the lamp, thus is
much lower than the radiation efficiency, that is, the ratio of the
power of the visible to the total radiation.
Thus the efficiency of the carbon arc is considerably increased
by reducing the loss by heat conduction, by the use of smaller
carbons — the life of the carbons, however, is greatly reduced
thereby, due to their more rapid combustion.
The carbon arc lamp thus gives the most efficient incandescent
light, as it operates at the highest temperature, the boiling point
of carbon. But by doing so the radiator is continuously con-
sumed and has to be fed into the arc. This requires an operating
mechanism and becomes feasible only with large units of light.
To attain the highest possible efficiency of light production by
temperature radiation with a permanent radiator, thus requires
the use of extremely refractory bodies, since the efficiency in-
creases with the increase of the temperature, and is still very
low at the melting point of platinum.
To exclude all the losses of energy by heat conduction and
heat convection, the radiator is enclosed in a vacuum, so that all
the power input is converted into radiation. Even in this case
the efficiency of light production is still relatively low.
The vacuum used in the incandescent lamp, thus, is not only
for the purpose of protecting the filament from combustion.
Filling the globe with some gas which does not attack the carbon
would do this and yet it would very greatly lower the efficiency,
TEMPERATURE RADIATION.
77
as can be seen by admitting air into the lamp bulb, when the
filament drops down to dull red heat, before it burns through.
With a metal filament lamp this can be seen still plainer, as the
filament lasts longer in air.
A search, thus, has been made and is still being made, through-
out the entire range of existing bodies, for very refractory mate-
rials. Such materials may be chemical elements or compounds.
However, the combination of a refractory element with one of
very much lower melting point lowers its melting point, and very
refractory compounds, thus, may be expected only amongst the
combinations of very refractory elements with each other.
The chemical elements, arranged in order of their atomic
weight, exhibit a periodicity in their properties which permits
FIG. 28.
a systematic study of their properties. In diagram Fig. 28 the
elements are arranged in order of their atomic weight in the
"periodic system."
The height of their melting point is indicated by the darkness
of the background. That is, the most refractory elements,
wolfram and carbon, are shown on black background. The ele-
ments of somewhat lower, but still so very high melting point
that they cannot be fused by any temperature attainable by
combustion, but require the electric furnace, are shown on cross
shaded background. Inversely, the elements of the lowest melt-
ing point, mercury under the metals and helium under metal-
78 RADIATION, LIGHT, AND ILLUMINATION.
loids, are shown on white background, and the easily fusible
metals and gaseous metalloids on lightly shaded background.
As seen, there are two peaks of refractoriness, one amongst the
metalloids, in carbon, and one under the metals in wolfram (or
tungsten), and around these two peaks all the refractory elements
are grouped. Inversely, there are also two depressions, or points
of minimum melting point, in helium under the metalloids,
around which all the gaseous elements are grouped, and in mer-
cury under the metals, around which all the easily fusible metals
are grouped.
It is interesting to note that the melting point rises towards
wolfram from both sides, as diagrammatically illustrated at the
top of Fig. 28, in such a manner that the maximum point
should be expected in the space between wolfram and osmium
and the unknown element, which belongs in this space of the
periodic system, thus should be expected to have still a higher
melting point than wolfram, and thus give a higher efficiency of
light production.
As metal alloys almost always have lower melting points than
their most refractory element, very refractory compounds thus
may be expected only in the compounds between the very refrac-
tory elements, in which at least one is a metalloid, that is, amongst
the carbides and borides and possibly silicides and titanides.
37. Some of the earliest work on incandescent lamps was
carried out with metal filaments. Platinum and iridium, how-
ever, were not sufficiently refractory to give good efficiencies, and
the very refractory metals were not yet available in sufficient
purity. A small percentage of impurities, however, very greatly
lowers the melting point, especially with metals of very high
atomic weight. For instance, wolfram carbide contains only
3 per cent of carbon and 97 per cent of wolfram and even 0.5 per
cent of carbon in wolfram metal thus means that 16 per cent of
the metal consists of the easily fusible carbide.
Very soon, therefore, metal filaments were abandoned and car-
bon used as lamp filament. While carbon is the most refractory
body, remaining solid up to 3750 deg. cent., it was found that the
carbon filament could not be operated much above 1800 deg. cent,
without shortening the life of the lamp below economic limits by
the evaporation of the carbon and the resulting blackening of the
lamp globes. All bodies evaporate below their melting point.
TEMPERATURE RADIATION. 79
Thus water evaporates considerably below the boiling point and
even below the freezing point : ice and snow gradually disappear
by evaporation even if the temperature never rises above the
melting point. Considerable differences, however, exist between
different bodies regarding their rate of evaporation. Thus water
and benzine have practically the same boiling point, but at the
same distance below the boiling point, benzine evaporates much
faster than water; that is, has a much higher vapor tension.
Carbon has a very high vapor tension, that is, shows a very rapid
evaporation far below the boiling point, and since in the incan-
descent lamp the carbon vapor condenses and is deposited on the
globe and carbon is black, it blackens the globe and obstructs the
light. Also, the decrease of the filament section by evaporation
increases its resistance and thereby decreases the power consump-
tion and so still "further lowers the efficiency. While, therefore,
carbon remains solid up to 3750 deg. cent., at about 1800 deg.
cent, its rate of evaporation is such as to lower the candle power
of the lamp by 20 per cent in 500 hr. life, and at this tempera-
ture it gives only an output of one candle power for 3.1 watts
input. Operating the carbon filament at higher temperature
would increase the efficiency and thus reduce the cost of energy
for the same amount of light, but would decrease the useful life
of the lamp and, therefore, increase the cost of lamp renewals, and
the most economical operation, as determined by balancing the
cost of lamp renewals against the cost of energy, is reached by
operating at such temperatures that the candle power of the lamp
decreases by 20 percent within 500 hr. life. The life of a lamp
down to a decrease of candle power by 20 per cent, thus, is called
the useful life, and when comparing the efficiencies of incandescent
lamps it is essential to compare them on the basis of the same
length of useful life: 500 hours with the carbon filament, since
obviously by shortening the life higher efficiencies could be
reached in any incandescent lamp. The operating temperature
of the carbon filament lamp, thus, was limited by the vapor ten-
sion of carbon and not by its boiling point.
This limitation of carbon lead to the revival of the metal fila-
ment lamps in recent years. First arrived the osmium lamp,
with 1.5 watts per candle power. The melting point of osmium is
very high, but still very much below that of carbon, but the vapor
tension of osmium is very low even close to its melting point, so
80 RADIATION, LIGHT, AND ILLUMINATION.
that osmium could be operated at temperatures far closer to its
melting point without appreciable evaporation; that is, without
blackening and falling off of candle power, or, in other words,
could be run at a temperature from which carbon was excluded
by its too rapid evaporation. Osmium, however, is a very rare
metal of the platinum group, and found only in very limited
quantities in very few places and is one of those substances of
which no search could very greatly increase the supply, and while
one pound of osmium is sufficient for some 30,000 filaments, the
total amount of osmium which has ever been found on earth
would not be sufficient for one year's supply of incandescent
lamps. Osmium, therefore, was excluded from general use by its
limited supply.
The metal tantalum does not have quite as high a melting point
as osmium, hence can be operated only at 2 watts per candle
power. Tantalum also is a very rare metal, but, unlike osmium,
it is found in very many places, though in small quantities, but
it is one of those substances, like the rare earth metals used in
the Welsbach mantel, of which it seems that the supply could be
infinitely increased when required by the industries and the prices
thus would go down with the demand, just as has been the case
with the rare earths of the Welsbach mantel.
Last of all, however, was made available the most refractory of
all metals, wolfram or tungsten, and as lamp filament permitted
to lower the specific consumption to 1 to 1.25 watts per
candle power, that is, higher than any other incandescent radia-
tor. Wolfram melts far lower than carbon, probably at about
3200 deg. cent., but far above the temperature to which the car-
bon filament is limited by evaporation, and having practically no
vapor tension below its melting point, it can be operated far
above the temperature of the carbon filament, and thus gives a
much higher efficiency. Tungsten (or rather wolfram, as the
metal is called, tungsten is the name of its ore) is a fairly common
metal, its salts are industrially used to a very large extent for
fire-proofing fabrics and its supply practically unlimited.
These metal filaments thus differ from the carbon filament in
that their temperature is limited by their melting point and not
by evaporation, as is the case with the carbon filament, and thus
their useful life is usually ended by the destruction of the filament
by melting through at some weak spot, but not by blackening.
TEMPERATURE RADIATION. 81
These filament lamps do not blacken the globe, except when the
vacuum is defective or becomes defective, and by the residual
gases in the lamp globe volatile compounds are formed, as tungs-
ten oxide, which then deposits on the globe and terminates the
life of the lamp. Even then their blackening is characteristically
different from that of the carbon filament, in that it occurs very
rapidly, and the lamp, after running possibly for hundreds or
thousands of hours without blackening, suddenly blackens
within a few days and thereby becomes inoperative, while
with the carbon filament the blackening is gradual throughout
the life.
38. By the use of these refractory metals the efficiency of
light production by temperature radiation has been greatly
increased, by permitting the use of higher temperatures in the
radiator than were permissible with the carbon filament due to
its evaporation. However, regarding the rate of evaporation,
different modifications of carbon show very different characteris-
tics. The carbon filaments first used in incandescent lamps were
made by carbonizing vegetable fiber, as bamboo, or by squirting
a solution of cellulose through a small hole into a hardening solu-
tion and carbonizing this structureless horn-like fiber. These
filaments had a very high vapor tension, thus could not be run
as hot as the modern carbon filament and so gave a lower effi-
ciency. They are now used only as base filaments, that is, as
core on which a more stable form of carbon is deposited. Such
a form of carbon was found in carbon deposited on the filament
by heating it in the vapor of gasolene or other hydrocarbons.
This carbon deposit is of much lower electric resistance than the
base on which it was deposited, its negative temperature coeffi-
cient of electric resistance is lower and its vapor tension so much
lower as to make it possible to operate the lamp at a specific con-
sumption of 3.1 watts per candle power. Of late years a still
more stable form of carbon has been found in the so-called "me-
tallic carbon," produced from the gasolene deposited carbon shell
of the filament, by exposing it for several minutes to a tempera-
ture at the boiling point of carbon; that is, the highest attainable
temperature in an electric carbon tube furnace. Hereby the
gasolene deposited carbon of the filament shell — the inner base
does not appreciably change its characteristics — acquires metal-
lic characteristics: a low electric resistance, a positive tempera-
82 RADIATION, LIGHT, AND ILLUMINATION.
ture coefficient of electric resistance, metallic luster and elasticity
and very low vapor tension, so that it can be run at higher tem-
perature corresponding to a specific consumption of 2.5 to 2.6
watts per candle power, with very little blackening. These metal-
lized carbon filament lamps exhibit characteristics similar to the
metal filament lamps; their life is largely limited by breakage
and not by blackening.
Whether hereby the possibilities of carbon are exhausted or
still more stable forms of carbon will be found, which permit
raising the filament temperature as near to the boiling point of
carbon as the temperature of the wolfram filament is to its melt-
ing point * and thereby reach an efficiency superior to that of the
tungsten lamp, remains to be seen, but does not appear entirely
impossible. Carbon exists in a number of "allotropic" modifi-
cations of very different characteristics (similar to phosphorus in
"yellow phosphorus," "red phosphorus" and " metallic phos-
phorus") to a greater extent than any other element, probably
due to the tendency of the carbon atom to join with other carbon
atoms into chains and rings, which tendency is the case of the
infinite number of carbon compounds. These form two main
groups : the chain carbon derivates (methane-derivates) and the
ring carbon derivates (benzol derivates). The latter are far
more stable at high temperatures, since the breakage of the mole-
cule by temperature vibration is less liable in a ring structure
than a chain : a single break splits the molecule in a chain forma-
tion, while with a ring formation it still holds together until the
break closes again. Chain hydrocarbons at higher temperatures
usually convert to ring hydrocarbons. It is, therefore, reasonable
to assume that the carbon skeleton left by the carbonization of
the hydrocarbons also may exist in either of the two characteris-
tic atomic groupings : as chain carbon and as ring carbon, and
that the latter exhibits a much greater stability at high tempera-
ture than the former, that is, a lower vapor tension. Cellulose
is a chain hydrocarbon, and as in carbonization it never passes
through a fluid state, the molecular structure of its carbon atom
probably remains essentially unchanged. Thus the base fila-
* As carbon boils, at atmospheric pressure, below its melting point, and the
limiting temperature is that at which the filament ceases to be solid, with
carbon the limit is the boiling point temperature, while with tungsten it is
the melting point.
TEMPERATURE RADIATION. 83
ment would be a chain carbon, and its low stability and high vapor
tension, that is, the ease of breaking up of the molecules by
evaporation, thus would be accounted for.
A carbon compound, however, which passes through the vapor
state in carbonization, as the gasolene vapor in treating the car-
bon filament, would as vapor at high temperature largely convert
into ring structures, that is, benzol derivates, and thus give a car-
bon deposit consisting largely of molecules in which the carbon
atoms are grouped in rings. These molecules, therefore, are more
stable at high temperatures, and thus exhibit the lower vapor
tension shown by the gasolene deposited coating of the base
filament. This deposited carbon, however, must be expected to
have numerous side chains attached to the ring nuclei of the
molecules, and the side chains are relatively easily split off at high
temperatures, as is well known of the benzol derivates. As a
result thereof, this form of carbon, which I may call " interme-
diate carbon," still shows a considerable vapor tension, due to
the side chains of the ring structure. Exposure to extremely
high temperatures splits off these side chains, which then re-
arrange into the only form of carbon stable at these very high
temperatures; that is, ring structure and the "metallic" form of
carbon produced from the gasolene deposited carbon by the elec-
tric furnace, thus would be the ring structure of the carbon
molecule, that is, the condensation of numerous rings, similar to
that found in anthracene, etc. It, therefore, would have a very
high stability at high temperature; that is, be difficult to split up
and thus show the low vapor tension characteristic of the me-
tallic carbon. In other words, the high vapor tension of most
forms of carbon would be the result of the dissociation of com-
plex carbon molecules of chain structures, or of side chains of
ring structures, and a carbon atom of complete ring structure
thus would only show the vapor tension corresponding to the
molecular weight, which is very high, due to the large number
of atoms in the molecule.
Thus two characteristic allotropic modifications of carbon may
exist besides the transparent carbon or diamond :
(a)^ Chain carbon: high resistance, negative temperature co-
efficient of electric resistance, non-metallic character, high vapor
tension at moderate temperature.
(6). Ring carbon: low resistance (within the range of
84 RADIATION, LIGHT, AND ILLUMINATION.
metallic resistivities), positive temperature coefficient of re-
sistance, metallic character, low vapor tension at high tem-
peratures.
The latter one, obviously, is best suited as an incandescent
radiator.
It may be possible to introduce into the ring structure of the
carbon molecule other atoms of very refractory nature, as boron,
titanium, silicon, and by their chemical affinity still further in-
crease the stability of the molecule, so that it does not appear
outside of the possibility to find a form of carbon which as radia-
tor would be superior to any metal filament.
39. Most bodies show the same characteristic in their tempera-
ture radiation; that is, the total radiation varies in the same man-
ner with the temperature as the fourth power of the absolute
temperature. Thus the distribution of the frequencies in the
radiation is the same for the same temperature, varies in the same
manner with the temperature, so that the distribution of the
radiation power between the different frequencies is a charac-
teristic of the temperature, independent of the material of the
body, and can be used for determining the temperature of the
radiator.
Such bodies, therefore, are said to give normal temperature
radiation.
Many bodies of normal temperature radiation give the same
intensity, or power of radiation, at the same temperature, that is,
have the same radiation constant k in equation (1) ; these bodies
are called " black bodies," and their radiation " black body radia-
tion." Their radiation is the maximum temperature radiation
given by a body. Other bodies of normal radiation give a lower
intensity or radiation, but so that their radiation is at any tem-
perature and for any frequency the same fraction of the radiation
of a black body. Their radiation, then, is called "grey body
radiation," and they also would follow the radiation law equa-
tion (1), but with a constant k, which is a fraction of the constant
kQ of black body radiations :
k = bkQ.
For temperature radiation the following law applies :
"The temperature radiation of a body is at any temperature
and at any frequency the same percentage of black body radiation
TEMPERATURE RADIATION. 85
as the absorbed radiation of the body is of the total impinging
radiation." (KirchhofTs law.)
This law relates the behavior of a body towards radiation
impinging upon it from other bodies, with its behavior as radiator.
A body which absorbs all the impinging radiation, that is, a
black body, gives a maximum temperature radiation, and this
radiation, thus, has been called the black body radiation. An
opaque grey body of albedo a, that is, a body which reflects the
same fraction a of the impinging radiation and thus absorbs the
part (1 — a) of the impinging radiation, thus gives as radiator
the part (1 - a) of black body radiation. That is, its radiation
constant is
k = bk0 = (1 - a) fcc,
and the radiation constant of any opaque body, thus, is the radia-
tion constant of the black body multiplied by 1 minus its albedo a.
For a perfectly white or perfectly transparent body, the radia-
tion constant, thus, would be zero; that is, this body would give
no temperature radiation, would not become incandescent at
high temperatures.
40. A colored body was defined as a body which reflects or
transmits different fractions of the impinging radiation for dif-
ferent frequencies. Such a colored body usually absorbs different
parts of the impinging radiation for different frequencies and as
radiator, then, would for different frequencies give different frac-
tions of black body radiation; that is, its radiation for some
frequencies would be a greater part of black body radiation. The
radiation of such a body is called "colored body radiation." In
colored body radiation the distribution of intensities throughout
the spectrum, that is, for different frequencies, thus differs from
that of the black or grey body at the same temperature, that is,
colored radiation is not normal radiation and thus also does not
follow the temperature law equation (1).
For instance, if in Fig. 29, 1 is the curve of distribution of the
intensity of radiation as function of the frequency, at a certain
temperature, as the melting point of tungsten, for a black body;
grey body radiation would be represented by curve II or III, in
which the ordinates are a constant fraction of those of curve I.
Curve II, for albedo a = 0.3, has the height 1 - a = 0.7 times
that of black body radiation I, that is, radiates 70 per cent as
86
RADIATION, LIGHT, AND ILLUMINATION.
much energy, at any temperature and of any frequency, as a black
body. Curve III corresponds to albedo a = 0.6, or a radiation
constant 1 - a = 0.4 times that of the black body. Colored
body radiation, then, would be represented by curves IV and V.
Representing the gctave of visible radiation by L, the area of
the curve within the limits of L to the total area of the radiation
curve, gives the ratio of power visible to total radiation, or the
" radiation efficiency." As seen, this radiation efficiency is the
same for black and grey bodies, I, II, III, and the only difference
between the black and the grey body is that with the grey body
the amount of light per unit radiating surface is less, but the
7
\
\
\
\\
FIG. 29.
power required to maintain the temperature is correspondingly
less, hence the efficiency is the same and merely a larger radiator
surface required to produce the same amount of light ; the larger
the surface, the higher the albedo of the radiator. For colored
radiators, however, the radiation efficiency may be different and
frequently is. In the colored body IV, in which the radiation in
the visible range is a greater part of the black body radiation I
than in the invisible range, the radiation efficiency is greater than
that of colorless or normal radiation at the same temperature ;
that is, such a colored body gives a higher efficiency of light
production than corresponds to normal radiation at the same
temperature. Such, for instance, is the case with the material of
TEMPERATURE RADIATION. 87
the Welsbach mantel. Inversely, the colored body V, in which
the radiation in the visible range is a lower percentage of black
body radiation than in the invisible range, gives a lower efficiency
of light production. Such, for instance, is the case with glass,
which, therefore, would be an abnormally inefficient incandescent
light producer.
To illustrate the difference in the radiation of black and grey
bodies, I show you here a piece of graphite rod, around which a
strip of platinum foil is wrapped in an open spiral and then it is
enclosed in a transparent quartz tube. Heating it in the bunsen
flame, you see the graphite becomes bright red, while the platinum
foil surrounding it is far less luminous and the quartz tube is not
luminous at all, though all three have practically the same temper-
ature, or if anything, the outer quartz tube is the hottest, the
interior graphite rod the coolest. Still, the graphite gives the
greatest amount of light : graphite is a black body and thus gives
maximum radiation; the platinum as a grey body gives less radia-
tion at the same temperature and the quartz as a transparent
body which absorbs almost no radiation, thus, also, gives out
almost no radiation, that is, does not become luminous at a
temperature at which the graphite is bright red.
I now drop a small platinum spiral into a mixture of the nitrates
of thoria and ceria (the rare earths of the Welsbach mantel), and
then immerse it in the bunsen flame. The nitrates convert to
oxides, which fluff out into a very light and porous mass, which
you see glow in a very intense, slightly greenish light, far brighter
than the platinum wire immersed in the same flame. The dis-
tribution of intensity of this radiation differs from that corre-
sponding to any temperature, and the percentage of visible
radiation, especially from the center of the visible spectrum
(greenish yellow) , is abnormally large. This, therefore, is a colored
radiator, giving a higher radiation efficiency than the normal
temperature radiation.
A radiation which does not follow the temperature law of
normal radiation as regard to the distribution of intensity with
the frequency, is called " selective radiation." Colored body
radiation, thus, is selective radiation.
In regard to their reaction on light impinging on them, in reflect-
ing or transmitting it, most bodies are more or less colored and
colorless bodies: black, grey, white, transparent, the exception.
88 RADIATION, LIGHT, AND ILLUMINATION.
Regarding the temperature radiation produced by the body as
radiator, most bodies are colorless, black or grey bodies, that is,
give normal radiation or nearly so, and colored or selective radia-
tion of appreciable intensity is the exception.
Obviously, no perfectly black, or even perfectly colorless radia-
tor exists, but even carbon shows a slight selectivity, a slightly
greater intensity of radiation at the red end of the spectrum than
corresponds to the temperature.
Perfectly black body radiation, "however, is the radiation at
the inside of a hollow body of uniform temperature, and the
laws of black body radiation, thus, are studied on the radiation
in the interior of a closed shell with opaque walls of uniform
temperature.
In the interior of such a hollow body of uniform temperature
every surface element radiates to every other element and receives
radiation from every other surface element, that is, the surface
element Al receives as much radiation from element A2 as ele-
ment A2 receives from Ar
Of the radiation received by a surface element Al by the radia-
tion law, that part which exists in the radiation produced by A1
is absorbed, that part which does not exist in the temperature
radiation of Av is reflected, and the total radiation issuing from
Ax, the radiation produced by it plus that reflected by it, together,
thus, make up complete black body radiation. If, then, the hol-
low radiator is a black body, it absorbs all the impinging radia-
tion, reflects none, and the radiation issuing from it thus is the
black body radiation produced by it. If the radiator is not
a black body, buj a grey or a colored body, of any frequency of
radiation, for which it has the albedo a, only the part (1 — a)
is produced by it, but the part a of the impinging radiation of
this frequency is reflected, and the total radiation of this fre-
quency, thus, still is unity, that is, back body radiation.
Obviously, the body cannot be perfectly closed, but must
contain an opening, through which the interior radiation is
observed, but if this opening is sufficiently small it introduces no
appreciable error.
The production of black body radiation from the interior of a
hollow body obviously requires that the walls of the body be
opaque; that is, that all the radiation produced inside of it is
either absorbed or reflected, and also depends on the condition
TEMPERATURE RADIATION. 89
that all the frequencies of black body radiation are present, since
evidently, no frequency which is entirely absent in the radiation
of the body could be produced by reflection. Furthermore, all
the radiation must be temperature radiation, that is, no lumines-
cence exist in the interior of the body. These requirements are
easily fulfilled, except at extremely high temperatures.
41. The radiation laws offer a means of measuring tempera-
ture, and the only means for those very high temperatures where
the gas thermometer (that is, the measurement of temperature by
the expansion of a gas) and the thermo-electric couple or the
resistance pyrometer cannot longer be used, as no material exists
which remains solid at temperatures such as those of electric
furnaces, etc.
As the total intensity of the radiation varies with the fre-
quency, and the ratio of the intensity of radiation of any definite
frequency to the total radiation, or the ratio of intensities at
two different frequencies of radiation, is a function of the tem-
perature, either can be used for measuring the temperature.
For instance, measuring the intensity of the total radiation —
which in vacuum enclosed radiators as incandescent lamp fila-
ments is done by measuring the power input — gives the tem-
perature if the body is a black body and its radiating surface
measured. If one temperature is known, as, for instance, by the
melting point of some substance, by comparing the total radia-
tion power with that at the known temperature, other tempera-
tures can be measured.
Determining the ratio of the power of the visible radiation,
and that of the total radiation — that is, the radiation efficiency
— thus gives the temperature for black bodies as well as grey
body radiators.
By comparing the intensity of any two radiations we get the
temperature. This can be done very easily by using two wave
lengths of radiation in the visible range. For instance, the ratio
of the intensity of the yellow and the blue radiation gives the
temperature. Resolving, then, the radiation by a prism P in
Fig. 30, into a spectrum, and by a shutter $t cutting out a
definite width of yellow and of blue light, and combining these
again by the mirror Ml and M2 we get a resultant green color
which is intermediate between yellow and blue, and the nearer to
the blue, the higher the temperature. Arranging, then, the mov-
90 RADIATION, LIGHT, AND ILLUMINATION.
able shutter S2 below Sl with a single opening, we can by it cut
out a single green color, and by moving the shutter S2 bring this
to coincidence in shade with the resultant color of shutter Sv and
the position of the shutter S2 then measures the temperature.
The scale of such a direct vision pyrometer may either be calcu-
lated from the radiation laws, or it may be calibrated by some
known temperatures, as the melting points of gold, platinum,
boiling point of carbon, etc.
A number of types of such visual pyrometers have been devel-
oped, and are very convenient.
Their limitation, obviously, is that they apply only when the
radiation is normal temperature radiation, but give wrong results
where colored radiation or luminescence is present. Thus the
FIG. 30.
radiation given by the interior of a closed body of uniform tem-
perature ceases to be black body radiation if the interior is filled
with luminous vapors, as is frequently the case in the interior of
electric furnaces. For instance, using such a visual pyrometer
for the interior of the carbon tube furnace used for metallizing
carbon filaments gives, frequently, quite impossible results, tem-
peratures above those of the sun, due to the error caused by the
luminescent silicon vapor filling the tube.
The errors of temperature measurements by radiation are the
greater the nearer together the radiation frequencies are which
are used for the measurement, hence are greatest with the visual
pyrometers, least in the methods based on the total radiation
power.
42. In the temperature radiation of a colored body the ratio
of the intensity of the radiation to that of a black body of the
TEMPERATURE RADIATION. 91
same temperature is different for different frequencies of radia-
tion, and the average wave length of radiation and the total
intensity of radiation of a colored body thus do not vary with the
temperature in the same manner as is the case with the black and
the grey body, that is, the normal radiation. The intensity of
colored body radiation at any frequency cannot exceed the inten-
sity of radiation of a black body at the same temperature and
frequency, since the radiation of the black body is the maximum
temperature radiation at any temperature and frequency.
A body which gives at any frequency a greater intensity of
radiation than a black body of the same temperature is called
luminescent, that is, said to possess "heat luminescence." Char-
acteristic of heat luminescence, thus, is an excess of the intensity
of radiation over that of a black body of the same temperature for
some frequency or range of frequencies, and the color of lumin-
escence is that of the radiation frequencies by which the lumin-
escent body exceeds the black body.
It is not certain whether such heat luminescence exists.
The high efficiency of light production of the Welsbach man-
tel, of the lime light, the magnesium flame, the Nernst lamp, etc.,
are frequently attributed to heat luminescence.
The rare oxides of the Welsbach mantel, immersed in the
bunsen flame, give an intensity of visible radiation higher than
that of a black body, as a graphite rod, immersed in the same
flame, and if we assume that these oxides are at the same tempera-
ture as the flame in which they are immersed, their light must be
heat luminescence and not colored radiation, as the latter can-
not exceed that of a black body. It is possible, however, that
these oxides are at a higher temperature than the flame surround-
ing them, and as the radiation intensity of a black body rapidly
rises with the temperature, the light radiation of the rare oxides,
while greater than that of a black body of the flame temperature,
may still be less than that of a black body of the same tempera-
ture which the oxides have, and their radiation, thus, colored
temperature radiation and not luminescence. Very porous
materials, as platinum sponge, absorb considerable quantities of
gases, and by bringing them in close contact with each other in
their interior cause chemical reaction between them, where such
can occur, and thus heat and a temperature rise above surround-
ing space. Thus platinum sponge, or fine platinum wire, immersed
92 RADIATION, LIGHT, AND ILLUMINATION.
in a mixture of air and alcohol vapor at ordinary temperature,
becomes incandescent by absorbing alcohol vapor and air and
causing them to combine. The oxides of the Welsbach mantel,
as produced by the deflagration of their nitrates, are in a very
porous state, and thus it is quite likely that in the bunsen flame
they absorb gas and air and cause them to combine at a far more
rapid rate than in the flame, and thereby rise above the flame
temperature. An argument in favor of this hypothesis is, that
these oxides, when immersed in the bunsen flame in close contact
with a good heat conductor, as platinum, and thereby kept from
rising above the flame temperature, do not show this high lumi-
nosity. I have here a small, fairly closely wound platinum spiral
filled with these oxides. Immersing it in the bunsen flame you
see the oxides and the platinum wire surrounding them glow with
the same yellow light, but see none of the greenish luminosity
exhibited by the oxide when free in the flame, except at a few
points at which the oxide projects beyond and is not cooled by
the platinum spiral. The absence of a high selective luminosity
of these oxides, when heated electrically in a vacuum or in an
inactive gas, also points this way. The gradual decay of the
luminosity shown by such radiators may be due to their becoming
less porous, by sintering — this would account for the very rapid
decay of the light of the lime cylinder in the hydro-oxygen flame,
and the very small decay of the more refractory oxides in the
Welsbach mantel — but it also may be the general characteristic
of luminescence, as we have found in the discussion of fluorescence
and phosphorescence.
In favor of heat luminescence as the cause of the very high effi-
ciency of these radiators is, however, the similarity of the con-
ditions under which it occurs, with those we find in fluorescence
and phosphorescence. Just as neither calcium sulphide nor zinc
silicate nor calcium carbonate are fluorescent or phosphorescent,
when chemically pure, but the fluorescence and phosphorescence
are due to the presence of a very small quantity of impurities, as
manganese, so the pure oxides, thoria, erbia, ceria,donot give very
high luminosity in the bunsen flame, but the high luminosity is
shown by thoria when containing a very small percentage of other
oxides.
While the existence of heat luminescence in these rare oxides
is not certain, no theoretical reason exists against it, as at ordi-
TEMPERATURE RADIATION. 93
nary temperature we have in phosphorescence the same phenome-
non of the production of a radiation exceeding in intensity that
of a black body of the same temperature: the black body radia-
tion at ordinary temperature contains no visible rays, while that
of a phosphorescent body does. Heat-luminescence, thus, may
be considered as fluorescence at high temperature.
However, to some extent, the question of the existence of heat
luminescence depends upon the definition of luminescence, and
any colored radiation may be considered as heat luminescence of
a grey body. For instance, the radiation represented by curves
IV and V of Fig. 29, may be considered as colored temperature
radiation, as they are below black body radiation, curve I. But
as they exceed at some frequencies the curves of grey body
radiation II and III, they may also be considered as heat lumi-
nescence of a grey body. If, then, we compare such curves of
selective radiation, IV and V, with normal temperature radiation
of the same total intensity — that is, with a grey body radiation
of the same power at the same temperature — all such selective
radiation can be considered as heat luminescence.
While the term " luminescence" is usually applied only to
abnormally high radiation in the visible range, in its general
physical meaning it applies to abnormal radiation of any fre-
quency range, and curve V in Fig. 29, for instance, would be the
curve of a grey body, which luminesces in the ultra-red, while
curve IV would be that of a grey body, in which the heat lumi-
nescence is in the visible range.
In general, however, it is preferable to consider as luminescence
only such radiation as exceeds the black body radiation of the
same temperature, and this will be done in the following, while
radiations which differ in their frequency distribution from the
black body, without exceeding it in intensity, are considered as
colored body radiations.
LECTURE VI.
LUMINESCENCE.
43. All methods of producing radiation, and more particularly
light, other than the temperature radiation or incandescence, are
generally comprised by the name luminescence. Some special
cases of luminescence have already been discussed in the phe-
nomena of fluorescence and phosphorescence, represented by the
conversion of the radiation absorbed by a body into radiation of
a different wave length.
Usually luminescence at ordinary temperature, or at moderate
temperatures, that is, temperatures below incandescence, is called
fluorescence or phosphorescence.
Fluorescence and Phosphorescence.
Fluorescence is the production of radiation from the energy
supplied to and absorbed by the fluorescent body, while phos-
phorescence is the production of radiation from the energy stored
in the phosphorescent body. This energy may be derived from
internal changes in the body, as slow combustion, or may have
been received by the body at some previous time — as by
exposure to light a calcium sulphide screen absorbs the energy
of incident radiation, stores it in some form, and afterwards
radiates it.
Fluorescence and phosphorescence usually occur simulta-
neously : the energy supplied to such a luminescent body brings
about certain changes in the body — as vibrations of the atoms,
or whatever it may be — which cause the body to send out radia-
tion. As long as this energy is supplied, the radiation of the
body continues, that is, it fluoresces. The changes in the body
which make it luminesce, represent energy storage — the kinetic
energy of the luminescent vibration, etc. — and when the energy
supply to the body ceases, the radiation issuing from the body
does not instantly cease, but continues, with gradually decreasing
intensity, until the stored energy is dissipated : the body phos-
94
LUMINESCENCE. 95
phoresces. Inversely, fluorescent radiation probably does not
appear instantly at full intensity, as energy has first to be stored.
The persistence of the luminescence after the power supply has
stopped, as phosphorescence, is very short, except with a few
substances, where it lasts for days. Where the energy of phos-
phorescent radiation is supplied by the energy of chemical
change in the body — as with yellow phosphorus — obviously
the phosphorescence persists as long as these chemical changes
can occur.
The different forms of luminescence may be distinguished by
the character of the energy which is converted into radiation.
The conversion of radiation energy into radiation of different
wave length, either immediately, or after storage in the body,
thus may be called radio-fluorescence and radio-phosphorescence.
It was discussed in Lecture II.
The same bodies, exposed to an electric discharge in a vacuum
(Geissler tube or Crooke tube) show electro-luminescence, fluores-
cence as well as phosphorescence, and usually with the same
color as in radio-luminescence.
Thermo-luminescence is exhibited by some materials, as the
violet colored crystals of fluorite (CaFl2), which, when slightly
warmed, luminesce — it is this which gave the name "fluores-
cence" to the phenomenon.
Some solutions, when crystallizing, show light during the
formation of crystals, and thus may be said to exhibit a physical
phosphorescence.
Chemical phosphorescence is exhibited by yellow phosphorus
and its solutions, which in the air glow by slow combustion, at
ordinary atmospheric temperature. As the ignition point of
phosphorus, that is, the temperature where it spontaneously
ignites, is little above atmospheric temperature, the chemical phos-
phorescence of phosphorus occurs at temperatures a few degrees
below ignition; it ceases, however, at very low temperature.
The chemical luminescence, as shown by phosphorus, is not
an exceptional phenomenon, but many substances exhibit chemi-
cal phosphorescence at temperatures a few degrees below their
ignition temperature, as the result of slow combustion. With
those substances which have an ignition point above incandes-
cence, this cannot be observed, but it is observed, for instance,
in carbon bisulphide, CS2, which ignites spontaneously at about
96 RADIATION, LIGHT, AND ILLUMINATION.
180 deg. cent., and a few degrees below this temperature phos-
phoresces in air, by slow combustion.
A biological phosphorescence is shown by many forms of life:
some bacilli of putrefaction phosphoresce, and are the cause of
the faint glow occasionally observed in decaying food, especi-
ally fishes. Amongst insects, numerous sea animals of dif-
ferent classes, especially deep-sea animals, phosphorescence is
frequently met, but its origin, that is, the mechanism of light
production by the firefly, etc., is still unknown.
When splitting a sheet of mica, or shaking a well-exhausted
tube containing mercury, flashes of light are seen in the darkness.
This, however, is not real phosphorescence but due to electrostatic
flashes of frictional electricity.
The light given by fluorescence and phosphorescence of solids
or liquids, gives a continuous spectrum, that is, is a mixture of all
frequencies, just as is the case with temperature radiation; it
differs, however, from temperature radiation by the distribu-
tion of the energy in the spectrum, which is more or less charac-
teristic of the luminescent body, and to some extent, also, of the
method of exciting the luminescence. Thus crystalline calcium
tungstate, W04Ca, fluoresces white in the X-ray, light blue with
ultra-violet light; the aniline dye, rhodamine, 6 G, in alcoholic
solution fluoresces green in daylight, crimson in the light of the
mercury lamp; willemite (calcium silicate) shows a maximum
fluorescent radiation in the green, some chalcites in the red, etc.
So far, fluorescence and phosphorescence nave not yet found
any extended industrial application.
44. Some of the characteristic forms of luminescence at higher
temperatures are pyro-luminescence, chemical-luminescence, and
electro-luminescence.
As pyro-luminescence or heat-luminescence, must be considered all
radiation, produced by heat, which exceeds at some wave length
the intensity of the black body radiation at the same temperature.
Whether real pyro-luminescence exists, is uncertain, but by an
extension of the definition any colored temperature radiation
may be considered as heat luminescence of a grey body of an
albedo which as normal temperature radiation would give the
same total radiation at the same temperature as the colored
radiator. Heat luminescence has been discussed already under
colored radiation.
LUMINESCENCE. 1 97
Chemical Luminescence.
Whenever intense chemical changes take place at higher tem-
perature, luminescence frequently occurs. I have here an ordi-
nary, non-luminous bunsen flame. I dip a platinum wire into a
solution of lithium chloride, LiCl, and then hold it into the lower
edge of the flame: the flame colors a bright red, and through the
spectroscope you see a bright deep red line and a less bright
orange line, the spectrum of Li. After a little while, the color-
ing disappears by the LiCl evaporating from the wire, and the
flame again becomes non-luminous. I repeat the same experi-
ment, but dip the platinum wire into sodium chloride, NaCl,
solution, and you see the flame colored brightly yellow, and the
spectroscope shows one yellow line, the sodium line D. Dipping
the platinum wire into thallium chloride, T1C1, I color the flame
a bright deep green, the characteristic Tl spectrum, which has one
bright green line. As you see, the green coloring disappears
more rapidly than the yellow did, and the flame turns yellow;
the Tl salt is more volatile than the sodium salt, evaporates more
rapidly, and as it contains some Na as impurity, the latter be-
comes visible as yellow flame coloring after the Tl has evap-
orated.
In the bunsen flame these salts are evaporated, split up into
their elements by the flame gases, and recombine, and by these
chemical changes the atoms of Li, Na or Tl are set in vibration,
and as vapors, being free to vibrate without mutual interference,
they vibrate with their characteristic frequency, that is, give a
definite frequency and thus color of the light, independent of the
temperature; if we introduce the same salts into the carbon arc
we get the same color and the same spectrum lines, only much
brighter, as at the much higher temperature of the arc flame the
vibration is far more intense; but it is of the same frequency, and
in this respect essentially differs from temperature radiation
which varies in frequency with the temperature.
In the same manner by introducing Sr, Ba or Ca salts in
the bunsen flame, the flame is colored with other character-
istic colors; bright red, green, orange The spectroscope shows
in every case a spectrum having a number of definite lines
which are brightest and most numerous in the red for Sr, in the
green for Ba, and in the orange yellow for Ca. In general,
98 RADIATION, LIGHT, AND ILLUMINATION.
metal spectra show a number, frequently very many lines in
the visible range.
As Sr, Ba, Ca, are much less volatile than Li, Na, Tl, to get
good effects in the bunsen flame, instead of the chlorides, the
nitrates, or preferably the chlorates or perchlorates are used,
which are more unstable, and thus easier split up and carried into
the flame. At the much higher temperature of the carbon arc,
the chlorides, or even the still more refractory oxides are used.
Chemical luminescence is used industrially in fireworks and
colored signal lights; salts of these metals with acids which con-
tain a large amount of easily split off oxygen, as nitrates, or more
commonly chlorates and perchlorates, are mixed with some com-
bustible material, as charcoal, sugar, sulphur, antimony sulphide,
etc. When ignited, the combustible burns with the oxygen
given off by the nitrates or chlorates, and in the focus of this
intense chemical action, intense luminescence of the metal is
produced. Thus Sr gives a bright red, Ba a green, Ca an orange
yellow, copper ammon a blue coloring.
Electro-luminescence of Gases and Vapors.
45. Industrially this is the most important form of lumines-
cence. Solids and liquids can be made to luminesce only indi-
rectly by exposure to electric discharges, as electrical fluorescence.
Gases, however — and under gases here and in the following we
include vapors as, for instance, the carbon vapor, which is the
conductor in the carbon arc — become electro-luminescent by
being used as conductors of the electric current. It is a charac-
teristic of electric conduction of the gases that this conduction is
accompanied by the production of radiation, and in the electric
conduction of gases we thus find the means of a more direct
conversion of electric energy into radiation, and thus into light.
It is, therefore, in this direction that a radical advance in the
efficiency of light production would be possible, and the subject
of electric conduction of gases (including vapors) thus is of the
highest importance.
Two forms of electric conduction in gases exist: disruptive
conduction, as represented by the Geissler discharge or the elec-
trostatic spark, and continuous conduction, as represented by the
electric arc.
LUMINESCENCE. 99
Disruptive Conduction.
In disruptive conduction the conductor is the gas which fills the
space between the terminals, and in carrying the current is
made luminous. The color of the light and its spectrum is that
of the gas which fills the space, and the electrode material has no
effect on the phenomenon, is immaterial (in the Geissler tube,
or the spark gap, any material may be used as terminal, if it
•otherwise is suitable, that is, is not destroyed by whatever heat
is produced at the terminals, or by the chemical action of the gas
in the space, etc.) usually, however, the electrodes gradually dis-
integrate in disruptive conduction.
Disruptive conduction is discontinuous; that is, no current
exists below a certain definite voltage, while above this voltage
there is current. The voltage at which conduction begins is
called the disruptive voltage. It is the minimum supply voltage at
• which current exists : if the supply voltage rises above this value
there is current; if it drops below the disruptive voltage the
current ceases, but begins again spontaneously as soon as, the
voltage rises above the disruptive value. Disruptive conduction
thus occurs equally well with unidirectional, with alternating,
or with oscillating currents. It is best studied with alternating
or oscillating voltage supply, as with a steady unidirectional
voltage, the disruptive conduction, that is, conduction by the
gas filling the space between the electrodes, tends to change to
continuous conduction, by vapors forming at the negative elec-
trode and gradually bridging the space between the electrodes,
and thereby replacing the gas which fills the space, by the elec-
trode vapor as conductor. This is usually expressed by saying:
the electrostatic spark between two terminals starts, or tends to
start, an arc.
Disruptive conduction, thus, does not follow Ohm's law; it is
zero below the disruptive voltage, while with a supply voltage
exceeding the disruptive voltage of the gas between the terminals,
current exists, but the terminal voltage is apparently indepen-
dent of the current, that is, if the other conditions as temperature,
gas pressure, etc., remain the same, the terminal voltage of the
Geissler tube or the spark gap remains the same and independent
of the current, and the current is determined by the impedance
between the. Geissler tube or spark gap and the source of
100 RADIATION, LIGHT, AND ILLUMINATION.
e.m.f., or by the available power of the supply source. A Geissler
tube, thus, cannot be operated directly on a constant potential
supply of unlimited power, but requires a current limiting im-
pedance in series with it, or a source of limited power, that
is, a source in which the voltage drops with increase of cur-
rent, as a constant current transformer or an electrostatic
machine, etc.
The disruptive voltage essentially depends on the gas pressure
in the space between the electrodes, and also on the chemical
nature, and on the temperature of the gas. It is over a wide
range, directly proportional to the gas pressure. Thus, at n
atmospheres pressure the voltage required to jump a spark
between two terminals is n times as great as at one atmosphere.
This law seems to hold from the highest pressures which have
been investigated down to pressures of a few mm. mercury, that
is, down to about T^ atmosphere. When coming to still lower
pressures, however, the disruptive voltage decreases less, ulti-
mately reaches a minimum — usually somewhere between 1 mm.
and 0.1 mm. mercury pressure — and then increases again and
at extremely high vacua becomes much higher than at atmos-
pheric pressure, so that it seems that it is infinite in a perfect
vacuum, that is, no voltage can start conduction through a
perfect vacuum. As the gas filling the space is the conductor
in disruptive conduction, it is easily understood that in a per-
fectly inert space, or an absolute vacuum, no disruptive con-
duction would exist.
The visible phenomena of disruptive conduction very greatly
change with the change of gas pressure; from the electrostatic
spark at atmospheric pressures to the Geissler tube glow in the
vacuum; but the change is gradual, thus showing the identity
of the two phenomena. At atmospheric pressure, disruptive
conduction occurs by a sharply denned, relatively thin and noisy
spark of very high brilliancy, which traverses the space between
the electrodes in an erratic zigzag path, not unlike in appearance
to the mechanical fracture of a solid material; and, indeed, the
spark is an electrostatic rupture of the gas. If the electrostatic
field is fairly uniform, as between parallel plates, or between
spheres of a diameter 1.5 or more times their distance, with
gradual rising voltage, the spark occurs when the disruptive
voltage is reached, without being preceded, at lower voltage, by
LUMINESCENCE. 101
any other phenomenon. If, however, the electrostatic field is
not uniform, as, for instance, between needle points or small
spheres or wires, with increasing voltage the disruptive strength
of the gas is exceeded at those places where the field intensity is
highest, as at the needle points, before the disruptive voltage of
the spark gap is reached, and then a partial break down occurs
at the points of maximum field intensity, as at the needle points,
or at the surface of high potential conductors, etc. A blue glow,
then, appears at the needle points followed by violet streamers
(in air, the color being the nitrogen spectrum; in other gases
other colors appear), and gradually increases in extent with
increasing voltage, the so-called " brush discharge," or " corona."
Between needle points the brush discharges increase in extent,
and approach each other until they bridge nearly 60 per cent of
the gap, and then the static spark occurs.
At higher gas pressures the spark increases in brilliancy, in
noisiness, but gets thinner. If, however, we gradually decrease
the gas pressure, the spark gets thicker, less brilliant, and less
noisy, its edges are less sharply defined, that is, get more diffused,
and ultimately it passes between the terminals as a moderately
bright, thick and noiseless stream, gradually fading at its outside,
and at still higher vacua it fills the entire space of the vacuum
tube. At the same time the required voltage is decreased with
decreasing gas pressure, as discussed above.
46. I show you here (Fig. 31) the gradual change from the
static spark to the Geissler tube glow: in a closed glass tube G,
I have two needle-shaped terminals, 5 cm. distant from each other,
and supply them with energy from a small 33, 000- volt trans-
former. You see the oscillating static spark at atmospheric
pressure. By now exhausting the tube, while the voltage is
maintained at the terminals, you can watch the gradual change
from the static spark to the Geissler tube glow. In this experi-
ment, a small condenser, a Leyden jar, is shunted across the high-
potential terminals of the transformer, to guard against the
disruptive conduction changing to continuous conduction, that
is, to an arc, and a reactance inserted into the low-tension pri-
mary of the step-up transformer, to limit the discharge current,
as shown diagrammatically in Fig. 31.
If the Geissler tube has a considerable diameter, 3 to 5 cm.,
the Geissler discharge with alternating current is striated; that
102
RADIATION, LIGHT, AND ILLUMINATION.
is, disk-shaped bright spots with diffused outlines alternate with
less luminous spaces, about as shown in Fig. 32. The distance
between the luminous disks increases with decrease of the gas
pressure. Two sets of such disks exist, one issuing from the
one, the other from the other terminal. They are stationary
FIG. 31.
only if the gas pressure is perfectly constant, but separate and
contract with the slightest change of pressure, hence are almost
never at rest, but constantly moving through each other. The
two sets of disks, by passing through each other during their
motion, give rise to a number of different appearances. Some
of the successive shapes are shown in Fig. 32.
The voltage distribution in the space between the terminals,
in disruptive conduction, also: changes with the pressure- at
LUMINESCENCE.
103
atmospheric pressure, practically all the voltage is consumed in
the space between the terminals, and between needle points for
distances of 10 cm. and over very closely 4000 volts effective
alternating per cm. (10,000 volts per inch) are required (a 2-cm.
gap between needle points, however, requires 10,000 volts). With
II
II II
FIG. 32.
decreasing gas pressure the voltage consumed in the space be-
tween the terminals decreases,but the voltage consumed at the
terminals increases, and in a good Geissler tube vacuum with
nitrogen gas filling the space between the terminals, from 1000 to
3000 volts may be consumed at the terminals, while the voltage
consumed in the space between the terminals may drop as low
as 2 volts per cm.
The voltage consumed at the terminals seems to decrease v ith
increase of their size. The voltage consumed in the space be-
104 RADIATION, LIGHT, AND ILLUMINATION.
tween the terminals, that is, in the luminous stream of the Geiss-
ler tube, seems to be practically independent, not only of the
current, but also of the size of the tube, as should be expected
with a disruptive discharge. It varies, however, with the tem-
perature, and is different with different gases, that is, different
gases have different disruptive strength.
The light given by the Geissler tube shows the spectrum of the
gas, and thus is very bright and fairly efficient with a gas as nitro-
gen, which gives a large number of spectrum lines in the visible
range, and less efficient with a gas as carbon dioxide or hydrogen,
in which the lines in the visible range represent only a small part
of the radiated energy.
The industrial use of the electro-luminescence of discontinuous
conduction, that is, Geissler tube lighting, is still very limited
(Moore tube). So far only nitrogen gives a fairly good efficiency,
reaches apparently values between the tungsten lamp and the
tantalum lamp ; or, a specific consumption of two watts per mean
spherical candle power. The color of the nitrogen spectrum is
a golden yellow. As the range of gas pressure in which the
voltage is near the minimum is very narrow, and the gas pres-
sure changes during operation, by absorption at the electrodes,
etc., means have to be provided to maintain constant gas pressure
by automatically feeding gas into the tube whenever the pres-
sure drops below the minimum voltage or maximum efficiency
point. The greatest disadvantage of Geissler tube lighting,
however, is the high voltage required at the terminals. To get
fair efficiency the tube must be so long that the voltage con-
sumed in the stream — which represents the power converted
into light — is much larger than the voltage consumed at the
terminals — which represents wasted power. With a terminal
drop of 2000 volts, and two volts per cm. in the conducting gas
stream, to use half of the supply voltage for light production, thus
2000
requires a tube length of — — - = 1000 cm. = 10 m. or 33 feet,
2
and to use 80 per cent of the supply voltage for light production,
that is, waste only 20 per cent of the supplied power in heating
onrvrj
the terminals, requires a tube length of — — = 40 m. or 133 feet.
<L
Thus the Geissler tube as an illuminant is essentially a large unit
LUMINESCENCE. 105
of light, requiring high voltage (which obviously may be produced
by a transformer at the tube) and having a very great size. It
gives, however, low intrinsic brilliancy and splendid diffusion of
the light.
Continuous Conduction.
47. In continuous conduction, or arc conduction, the conductor
is a stream of electrode vapor, which bridges the gap between the
electrodes or terminals.
While in the spark, or the Geissler discharge, the conductor is
the gas which fills the space between the terminals, in the electric
arc the current makes its own conductor, by evaporation of the
electrode material, and maintains this conductor by maintain-
ing a supply of conducting vapor. The color and the spectrum
of the arc, thus, are those of the electrode material, and not of
the gas which fills the space in which the arc is produced, and
the nature of the gas in the space thus has no direct effect on
the arc. Its pressure obviously has an effect, as the vapor pres-
sure of the conducting arc stream is that of surrounding space,
thus increases with increasing gas pressure, and the arc vapor
then contracts, the arc gets thinner, while with decrease of the
gas pressure in the space surrounding the arc the vapor pressure
of the arc stream also decreases, thus the vapor expands, and
the arc stream becomes larger in section and correspondingly
less luminous.
As the arc conductor is a vapor stream of electrode material,
this vapor stream must first be produced, that is, energy must
first be expended before arc conduction can take place. An arc,
that is, continuous conduction, therefore, does not start spon-
taneously between the arc terminals if sufficient voltage is sup-
plied at the terminals to maintain the arc, but the arc has first
to be started, that is, the conducting vapor bridge produced by
the expenditure of energy.
If, therefore, in the arc the current ceases even momentarily,
the conduction ceases by the disappearance of the vapor stream
and does not start again spontaneously, but the arc has to be
started by producing a vapor stream. With alternating voltage
supply the arc, thus, would go out at the zero of current and have
to be started again at every half wave. In general, the arc, thus,
is a direct current phenomenon.
106 RADIATION, LIGHT, AND ILLUMINATION.
Some of the means of starting arc conduction are :
(1.) By bringing the terminals into contact with each other
and thereby closing the circuit, that is, establishing the current,
and then slowly separating them. In the moment of separation
the contact point is heated, vapor produced at it, and during the
separation of the terminals, a vapor stream is left behind as
conducting bridge. Obviously, if the terminals are separated
very rapidly, and the voltage is not much higher than required
to maintain the arc, not enough vapor may be produced to con-
duct the current, and the arc does not start.
(2.) By raising the voltage between the terminals so high that
a static spark passes between them, that is, disruptive conduction
occurs. The energy of this static spark, if sufficiently large, that
is, if the high voltage is maintained sufficiently long, then pro-
duces the vapor stream and starts the arc, that is, the arc follows
the spark. If the duration of the high voltage is very short, the
energy of the spark may not be sufficient to start the arc. Thus
high frequency discharges between live terminals frequently are
not followed by an arc, and the lower the voltage between the
terminals is, the more powerful a static spark is required to start
an arc.
(3.) By supplying the conducting vapor stream from another
arc, that is, by an auxiliary arc. If the vapor stream of this
auxiliary arc issues from the same terminal as the vapor stream
of the main arc which is to be started, only the normal operating
voltage is required in starting the latter arc, while a higher volt-
age is required, if the vapor is supplied by an entirely separate
arc.
(4.) By raising the space between the terminals to a very high
temperature, as by bridging the terminals by a carbon filament,
and by the passage of current raising this filament to very high
temperature.
48. The sharp distinction between the arc, in which the cur-
rent makes its own conductor by a vapor stream issuing from
the terminals, and the Geissler discharge, in which the current
uses the gas which fills the space as conductor, is best illustrated
by using in either case the same material, mercury, as conductor.
I have here a vacuum tube, shown to scale in Fig. 33, about 25.
cm. diameter, with three mercurv terminals. The tube has four
mercury terminals, of which, however, I use only three. The
LUMINESCENCE.
107
gas which fills the space between the terminals is mercury vapor.
1 now connect, as shown diagrammatically in Fig. 34, terminals
2 and 3 to the high potential coil of a step-up transformer — the
low potential circuit contains a reactance to limit the current -
and you see the striated Geissler discharge through mercury
FIG. 33.
vapor appear between terminals 2 and 3, giving the green light>
of the mercury spectrum. The terminals are quiet, as they do
not participate in the conduction. I now connect terminals 1
and 2 through a resistance, to 'a direct current supply, and tilt
the tube momentarily to let some mercury run over from 2 to 1,
and by thus momentarily connecting these terminals, establish
the current and so start the arc, and you see the mercury arc
pass between terminals 1 and 2, and see at one terminal — the
negative one — a rapidly moving bright spot, which marks the
point from which the vapor stream issues which carries the cur-
rent. We have here in one and the same vacuum tube, and
with the same material — thus, the same color and spectrum of
light, both types of conduction — the continuous high current and
low voltage conduction of the mercury arc, and the striated high
voltage low current disruptive conduction of the Geissler dis-
charge through mercury vapor.
The conducting vapor stream which carries the current in the
arc, at least in all arcs which so far have been investigated, issues
108
RADIATION, LIGHT, AND ILLUMINATION.
from the negative terminal or cathode, and is in rapid motion
from the negative towards the positive. The character of the
arc, therefore, is determined by the material of the negative
terminal, the temperature of the arc stream in general probably
is the temperature of the boiling point of the negative terminal,
3J=10 OHMS
FIG. 34.
and the spectrum of the arc is the spectrum of the negative ter-
minal. An exception herefrom, occurs only in those cases in
which the positive terminal contains material which boils below
the temperature of the arc stream (flame carbons) and the posi-
tive terminal is made so small that its tip is raised to the
temperature of the arc stream, and at this temperature heat
evaporation of the material of the positive occurs. These vapors
enter the arc stream, and there become luminous, possibly by
chemical luminescence, and add their spectrum to that of the arc
conductor, that is, the negative material. In this case the arc
spectrum shows the negative as well as the positive material, or
at least the more volatile components of the positive material.
LUMINESCENCE. 109
With the exception of this case of heat evaporation from the
positive terminal, the material of the positive terminal does not
participate in the phenomena occurring in the arc. Thus the
positive can be made of any conducting and refractory material,
and if made sufficiently large not to get too hot, does not con-
sume; only the negative terminal of the arc consumes in feeding
the arc flame, that is, supplying the vapor conductor, but the
positive is inherently non-consuming, and may be made a perma-
nent part of the arc-lamp mechanism. On the contrary, if the
positive is made so large that its temperature remains very much
below the arc temperature, condensation of the arc vapor occurs
at it, and it builds up, that is, increases in size. Consumption
of the positive terminal is thus due merely to the heat produced
at it by combustion or heat evaporation.
While the arc conductor issues from the negative terminal, in
general more heat is produced at the positive terminal. Thus
with both terminals of the same size and material, as usual in
the carbon arc, the positive gets hotter, and therefore in open
air burns off faster, which has led to the erroneous assumption
that the positive feeds the arc.
While carbon is the material most commonly used as termi-
nals, the carbon arc is not a typical arc, but is an exceptional arc.
(1) Because carbon is one of the very few substances which
change directly from the solid to the vapor state, that is, do not
melt at atmospheric pressure, but boil below the melting point.
(2) Carbon is the most refractory substance and the tempera-
ture of the carbon arc higher than the boiling point of any other
substance. Any material existing in the terminals of a carbon
arc thus evaporates, and by entering the arc stream shows its
spectrum, so that luminescent material can be fed into the carbon
arc from either terminal.
(3) At the temperature of the carbon arc all gases and vapors
have become good conductors, and a carbon arc thus can operate
equally well on alternating current as on direct current; that is,
the voltage required to maintain the carbon arc is. sufficient,
after the reversal of current, to restart it through the hot carbon
vapor.
A typical arc is shown in Fig. 35 as the magnetite arc,
with a lower negative terminal M consisting of magnetite,
the non-consuming upper terminal C of copper, and of such
110
RADIATION, LIGHT, AND ILLUMINATION.
size that it does not get so hot as to oxidize or evaporate,
but sufficiently hot to avoid condensation of magnetite vapor
on it.
The arc flame consists of an inner cylindrical core A, of bluish
white color and high brilliancy, slightly tapering at both ends,
which is surrounded by a less luminous shell B, of more yellowish
color, narrowest at the negative end, and increasing
in diameter towards the positive, surrounding the
latter.
The inner core A is the arc conductor, or con-
ducting vapor stream, while the outer shell B is
non-conducting luminous vapor, possibly containing
particles of solid material floating in it as incan-
descent bodies.
The arc conductor A issues from a depression S in
a melted pool P formed on the surface of the terminal
M. This depression S is in a rapid and erratic
motion, and thereby causes a constant and rapid
flickering of the arc. It is this flickering, inherent to
all arcs in which the negative terminal is fusible (which
therefore does not exist in the carbon arc), which has
retarded the industrial development of the more efficient metal
arcs until late years. Its cause is the reaction exerted by
the velocity of the vapor blast from the negative, which presses
the surface of the liquid pool down at the point from which
the current issues. The starting point of the current con-
tinuously climbs up the side of this depression, in shortening
the arc, but, in doing so, depresses its new starting point,
that is, the depression S, and thereby the negative end of the
arc stream moves over the surface the faster the more fluid
the surface is. In the mercury arc, this phenomenon of the
running spot at the negative terminal is also very marked, but
not so objectionable, as the arc stream is so long that the flicker
at the negative terminal has no effect on the total light. This
flickering disappears in the magnetite arc if we destroy the
fluidity of the melted magnetite by mixing with it some much
more refractory material, as chromite. The chromite remains
solid and holds the melted magnetite like a sponge. The reaction
of the vapor blast, then, cannot depress its starting point, and no
tendency exists of shifting the starting point, and the arc becomes
FIG. 35.
LUMINESCENCE.
Ill
steady. In this manner such arcs have now been made steady
and thereby suitable for industrial use.
49. Since the arc conduction issues as a rapidly moving vapor
stream from the negative terminal or cathode, it must be con-
tinuous at the cathode; if interrupted even for a very short time
at the cathode, a break exists in the continuity of the conductor
and conduction ceases, that is, the arc extinguishes. At any
other point of the arc stream, however, a break in the continuity
of the stream may exist, provided that current continues from
the negative, since such a break in the continuity of the con-
ducting vapor stream is bridged again, and conduction re-estab-
lished by the vapor stream coming from the negative. Thus the
FIG. 36.
arc can be started by merely starting a conducting vapor stream
from the negative, as by an auxiliary arc. As soon as this con-
ducting vapor reaches the positive terminal, it closes the circuit
and establishes conduction. An arc can be shifted or jumped
from one positive terminal to another one, but cannot be shifted
from negative to negative; the negative terminal, as the source
of the conducting vapor stream, must be continuous.
To illustrate this, I have here (Fig. 36) in a hand lamp two
copper rods A and B of about 5 mm. diameter, as arc terminals,
separated by 2.5 cm., and connected into a 220- volt direct-cur-
rent circuit, with sufficient resistances in series to limit the current
to about 4 amperes. A third copper rod of the same size, C,
is connected by a flexible lea.J to the upper terminal B. I close
the reversing switch S so as to make A negative, and B and O
, . '.. i \. , : ; ,- ,. . -
112 RADIATION, LIGHT, AND ILLUMINATION.
positive, and start an arc between A and C by touching C to A.
I draw this arc to about 4 cm. length, and without touching C
with B, as soon as the conducting vapor stream of the arc AC
(the inner core A of Fig. 35) touches B, as shown in Fig. 36, the
arc leaves C and goes to B, that is, by the arc AC I have started
arc AB. If I had separate resistances in series with the terminals
B and (7, the arc AC would also continue to exist after it started
arc AB- otherwise, as two arcs cannot run in parallel, the longer
arc, AC, goes out as soon as the shorter arc AB starts.
I now reverse the circuit by throwing switch S, and make A
positive, and B and C negative, again start AC by contact, and
draw it out until the arc flame wraps itself all around terminal
FIG. 37.
B} but the arc does not transfer. I even insert 10 ohms resist-
ance rl in series with C (Fig. 37), so that the voltage AB is about
40 volts higher than AC, that is, B by 40 volts more negative
than C, and still the arc does not transfer. I now touch C with
B and separate it again; if during contact the negative spot
during its motion happens to run over to terminal B, the arc con-
tinues between B and A; if, however, the negative spot has
remained on C, when separating again, the arc remains at C as
negative, although B is more negative by 40 volts.
An arc therefore can be started at its normal starting voltage
by an auxiliary arc having the same negative, but not by an
auxiliary arc with the same positive, and an arc can be shifted
from one positive to another, but not from one negative to
LUMINESCENCE.
113
another. The cause is, as explained above, the necessity of the
continuity at the negative terminal as the source of the conduct-
ing vapor stream.
Still more startling is the following demonstration : I shift the
resistance rl from C to B, and start the arc from A to B, with B
as negative, by bringing these terminals into contact with each
other, and then separating them. The auxiliary terminal C
(Fig. 38) now is by 40 volts more negative than the negative
terminal B of the arc. I now cut slowly through the arc stream
by moving C across it between A and B, as shown in Fig. 38:
the arc AB remains, but no current goes to C, although more
r =20 OHMS
ws
FIG. 38.
negative, that is, at a higher potential difference and a shorter
distance against A than B is. I even hold C for some time in
the conducting core of the arc AB, and still the current does not
shift from the negative B to the still more negative terminal C.
This experiment is interesting in demonstrating that a conductor
immersed into the arc flame does not assume the potential of the
arc flame, but may differ therefrom by considerable voltage, and
that it therefore is not feasible to determine the potential dis-
tribution in an arc by means of exploring electrodes, as has
frequently been attempted.
Obviously, if I now reverse the circuit, and make B and C
positive, A negative, the current leaves B and goes to C as soon
as C touches the conducting core of the arc AB.
50. The electric arc, therefore, is a unidirectional conductor,
that is, the vapor stream is conducting between its negative
114
RADIATION, LIGHT, AND ILLUMINATION.
terminal A in Fig. 36, that is, the starting point of the arc
stream, and any point reached by it which is positive to A, but
is non-conducting for any point which is negative with respect
to A.
If, now, in Fig. 38, with the terminal C immersed in the arc
stream, I connect A and C to a source of alternating voltage,
as shown in Fig. 39, while a direct-current arc flows from A to B,
with A as negative, then during that half-wave of the alternating
voltage, for which C is positive to A, there is current between A
and (7, while for the reverse half-wave, in which C is negative to
A, there is no current. The arc thus rectifies the alternating
voltage, and the rectification is complete, that is, there is
T= 30 OHMS
MAA
FIG. 39.
current during one half-wave only, but no current at all dur-
ing .the other. I show you this experimentally, using 50 volts
alternating between A and (7. With this arrangement, to
maintain the rectification continuously, obviously the ter-
minal C would have to be cooled.
Alternating voltage thus can be rectified by means .of the
unidirectional character of the arc : if a continuous vapor stream
is maintained from one terminal, either by direct-current ex-
citation or by overlapping several waves of alternating cur-
rent, current is in that direction only in which this exciter
terminal is negative, but not in the opposite direction.
. Such arc rectifiers — of which the mercury arc rectifier is the
most commonly used — have been developed and extensively
introduced in the industry, of la.te years, for operating, low-volt-
LUMINESCENCE.
115
age constant direct potential and high-voltage constant direct-
current circuits from a source of alternating voltage. Regarding
the electrical phenomena occurring in arc rectification, see
" Theory and Calculation of Transient Electric Phenomena and
Oscillations/' Section II, Chapter IV.
The inability of an alternating voltage to maintain an arc,
I show you here on the same apparatus by connecting the two
terminals (Fig. 40) A and B to the 1000-volt terminals of a
transformer — with sufficient resistance in series to limit the
current.
While 220 volts direct current easily maintained a steady
2-cm. arc between these terminals, with 1000 volts alternating
between the terminals, if I try to produce an alternating arc
by gradually separating the terminals, the circuit opens before
the terminals have separated 1 mm.; that is, 1000 volts alter-
nating cannot maintain an arc of 1 mm. between these copper
Fh
i = iu unM5
v— W
110 VJOLTS
60 CYCLES
FIG. 40.
terminals. The cause is obvious: to maintain an arc between
two terminals, a voltage is required sufficiently high to restart
the arc at every half-wave by jumping an electrostatic spark
between the terminals through the hot residual vapor of the
preceding half-wave. The voltage required by an electro-
static spark, that is, by disruptive conduction, decreases with
increase of temperature: for a 13-mm. (0.5-in.) gap, it is about
10,000 volts at atmospheric temperature, 7000 volts at the
boiling point of mercury (360 deg. cent.), 2500 volts at the
boiling point of zinc (1000 deg. cent.), 500 volts at the boiling
point of magnetite (2000 deg. cent.), 100 volts at the boiling
point of titanium carbide (3000 deg. cent.), 40 volts at the
boiling point of carbon (3500 deg. cent.). The voltage re-
quired to maintain a 13-mm. alternating arc must therefore be
116
RADIATION, LIGHT, AND ILLUMINATION.
Sit least as high as given by a curve somewhat like curve I in
Fig. 41 * (to bring the values of voltage within the scale of the
figure, the logarithm of voltage, as ordinate, is plotted against
the temperature as abscissa).
The voltage required to maintain an arc, that is, the direct-
current arc voltage, increases with increasing arc temperature,
and thereby increasing radiation, etc. For a 13-mm. (0.5-in.)
FIG. 41.
arc it is approximately shown as Curve II in Fig. 41 : 20 volts
for the mercury arc, 40 volts for the zinc arc, 60 volts for the
* As the disruptive voltage also depends on the chemical nature of the
vapor, that is, some gases and vapors have a higher disruptive strength than
others, as discussed above, the arrangement of the different materials regard-
ing their alternating arc voltages is not entirely determined by their boiling
points, but modified by individual characteristics. It further depends on the
current: at higher currents and thus larger amounts of residual vapor, the
voltage is lower. It further depends on the frequency: the lower the fre-
quency and the greater, therefore, the cooling effect during the reversal of
current the higher is the required voltage.
LUMINESCENCE. 117
magnetite arc, 75 volts for the titanium carbide arc, 80 volts
for the carbon arc.*
As seen from Fig. 41, the curves I and II intersect at some
very high temperature, near the boiling point of carbon, and
materials which have a boiling point above the temperature of
intersection of these curves require a lower voltage for restart-
ing the arc than for maintaining it, and a voltage sufficient to
maintain the arc restarts it at every half-wave of alternating
current, that is, such materials can maintain a steady alternat-
ing arc at the same voltage as a direct-current arc. Even
materials like titanium carbide, in which the starting voltage is
not much above the running voltage, maintain a steady alter-
nating arc, as in starting, the voltage consumed during running
in the steadying resistance or reactance is available.
Alternating arcs thus can be maintained at moderate volt-
ages only by a few materials of extremely high boiling points, as
carbon and carbides, but by far the largest number of materials
cannot be used as terminals of an alternating-current arc.
In Fig. 41 the range between the curves I and II is the
" rectify ing range," as in this range unidirectional current is
produced from an alternating source of voltage through the arc,
if the arc conductor is maintained by excitation of its negative
terminal. The voltage range of rectification thus is highest in
the mercury arc, which has the lowest temperature, and vanishes
in very high-temperature arcs. The carbon arc thus cannot
give complete rectification, while the mercury arc, or zinc arc,
etc., can do so. The mercury arc, having the greatest recti-
fication range, thus is practically always used for this purpose.
Below curve II of Fig. 41 no conduction occurs, between
curves I and II, unidirectional conduction takes place, and
above curve I, disruptive conduction and alternating current
can exist.
51. The light, and in general the radiation given by the arc
proper, that is, by the vapor conductor which carries the cur-
rent between the terminals, is due to luminescence, that is, to
a more or less direct transformation of electric energy into
* This voltage also is not merely a function of the arc temperature, but
modified somewhat by the chemical individuality of the material. It is a
function of the current and decreases with increase of current, so that above
values are approximate only, corresponding to about 4 amperes.
118 RADIATION, LIGHT, AND ILLUMINATION.
radiation, without heat as intermediary form of energy. The
quality or color of the light, or its spectrum, that is, the fre-
quency or frequencies of radiation given by the arc stream,
thus are not a function of the temperature, as in the radiation
produced by heat energy, but the frequencies are those at
which the luminescent body is capable of vibrating, that is,
are determined by the chemical nature of the luminescent body
or vapor conductor. The efficiency of light production thus
does not directly depend upon the temperature, does not in-
crease with increase of temperature, as in temperature radia-
tion, but to some extent rather the reverse. We have the same
relation as in other energy transformations: when converting
heat into other forms of energy, the more intense the heat,
that is, the higher the temperature, the higher efficiency we
may expect. When transforming, however, some form of
energy differing from heat, into another form of energy, as
mechanical into electrical energy, the heat produced repre-
sents a waste of energy, and the lower the temperature, the
higher in general, other things being equal, would be the effi-
ciency. The efficiency of light production by the arc thus is
not a function of the temperature, but the lowest temperature
arc, the mercury arc, is one of the most efficient.
The light given by the arc contains only a finite number of
definite wave lengths, that is, gives a line spectrum: very few
lines in the ordinary mercury arc, many thousands in the tita-
nium arc. The color of the light is essentially characteristic of
the nature of the luminescent body. For instance, it is white
in the titanium arc, as the lines of the titanium spectrum are
fairly uniformly distributed over the entire visible range. The
light of the calcium arc is orange yellow, as the spectrum lines of
calcium are more frequent and more intense in the orange-
yellow range of radiation, etc.
Frequently a change of the color of the luminescent light of
the arc occurs with the temperature, but it does not follow
a definite law, as in temperature radiation, but is a char-
acteristic particularity of the luminescent body: some of the
spectrum lines increase more rapidly in intensity, with increas-
ing temperature, than others, and the resultant color of the
light changes thereby. For instance, the ordinary iron arc, as
produced by 4 amperes direct current across a gap of 2 cm.
LUMINESCENCE. 119
between iron or magnetite terminals, and requiring about 75
volts, is white and very brilliant, that is, has a spectrum with
many lines about uniformly distributed over the visible range.
We can greatly increase the temperature of the arc by using a
high-frequency condenser discharge: in this case very large
currents of very short duration exist as oscillations between the
terminals, with periods of rest between the oscillations, very
long compared with the duration of the current. In this case
the duration of the current is too short to feed a large volume
of electrode vapor into the arc stream, and as the current is
very large during the short moment of the discharge, the
vapor between the terminals is very greatly overheated. Oscil-
lating condenser discharges thus offer a means of increasing the
temperature of the arc stream very greatly beyond the boiling
point of the material. When using a condenser discharge be-
tween iron terminals, we thus get an iron arc of very much
higher temperature, and this arc gives very little visible light,
but a very large amount of ultra-violet radiation. It is this
arrangement which we have used in the preceding to produce
ultra-violet light by the so-called " ultra-violet iron arc." In
the iron arc the average wave length of the radiation thus shifts
with increasing temperature to shorter wave lengths, or higher
frequencies, similar as in temperature radiation.
The reverse is the case with the mercury arc: the ordinary
mercury arc in an evacuated glass tube, with ample condensing
chamber, gives practically no red light; only a very powerful
spectroscope can discover some very faint red lines. If now
the condensation of the mercury vapor is made insufficient,
by obstructing ventilation, or greatly raising the current, or
omitting the condensing chamber in the construction of the
lamp, and the mercury vapor pressure and thereby the tem-
perature increased, at least three red lines located about as
shown in Fig. 42 become visible in the mercury spectrum even
in a low-power spectroscope,
Ill Oi i\J W IJ\J W Cl Ok-'CLiLlWO^V^lJC,
and increase in intensity with _J [ I
m v. ^ ,/ YELLOW <^^-^_ ^ BLUE VlO
increasing vapor pressure. To
show you this I use a U-shaped FlG- 42-
mercury lamp constructed as shown half size in Fig. 43. I con-
nect the lamp into a 220-volt direct-current circuit, with an
inductive resistance in series thereto, to limit the current, and
120
RADIATION, LIGHT, AND ILLUMINATION.
start the arc by pouring some mercury over from one side to
the other. Immediately after starting the lamp you see no red
lines in the low-power spectroscope which I have here. As with
the large current which I use — 3 amperes — the mercury vapor
cannot freely condense, the mercury vapor pressure rises and
FIG. 43.
presses the mercury level down in the center tubes, up in
the outside tubes, as indicated at b in Fig. 43, and thereby
enables us to measure the mercury pressure. Gradually you
see the three red lines appear, and increase in intensity, and
when the vapor pressure has risen to about 5 cm., the three
red lines are fairly bright, and numerous other red and orange
mercury lines have appeared. At this pressure we are so close
to the softening point of the glass that we cannot go further,
but by operating the mercury arc in a quartz tube, vapor pres-
sures of several atmospheres can be produced, and then the red
lines are very much more intense, many more lines have be-
come visible in the mercury spectrum, and the light is far less
greenish than the low-temperature mercury arc, more nearly
white.
Still much higher temperatures can be reached in the
mercury arc in an ordinary glass tube by using the condenser
discharge.
I have here, in Fig. 44, a mercury-arc tube with four
LUMINESCENCE.
121
terminals — the same which I used in Fig. 34 for showing
simultaneously the mercury arc and the Geissler discharge. I
connect terminals 3 and 4 to the high potential terminals of a
step-up transformer, but shunt a small condenser C across 3 and
4; you see, in the moment where I connect the condenser, the
previously existing green and striated Geissler discharge changes
r=so OHMS
3
r
%
\
\
-f-
JL2JUL&L
J>UP00Q
0000
roooo
T
III
1-^-40
1-7-40
1
r=.io OHMS
110 VOLTS
60 CYCLES
2 = 10 OHM
110 VOLTS
60 CYCLES
*m
FIG. 44.
to a bright pinkish-red arc, and the spectroscope shows that the
spectrum lines in the red and orange have greatly increased in
number, and have increased in intensity beyond that of the
lines in the green and blue, and the color of the light therefore
has changed from green, to pinkish red.
We have here in the same mercury tube shown diagram-
matically in Fig. 44 all three forms of luminescence of mercury
vapor: the high-current low-voltage, low-temperature arc of
122 RADIATION, LIGHT, AND ILLUMINATION.
uniform green color, from 1 to 2; the green high-voltage low-
current striated Geissler discharge, from 2 to 3, and the red high-
voltage mercury arc, from 3 to 4.
In the mercury arc, as result of the more rapid increase of
intensity of the red lines, the color of the light thus changes
with increase of temperature from bluish green at low tempera-
ture to white to red at very high temperature, that is, the aver-
age frequency decreases with increase of temperature, just the
reverse from what is the case with temperature radiation.
The change in the distribution of the power of radiation
between the different spectrum lines, with change of tempera-
ture, may increase the efficiency of light production — if the
lines in the visible range increase faster than in the ultra-red
and ultra-violet — or may decrease — if the visible lines in-
crease slower — or may increase in some temperature range,
decrease in some other temperature range, but all these changes
are characteristic of the luminescent material, and do not obey
a general law. Thus in the mercury arc the efficiency of light
production, with increase of temperature, rises to a maximum
at about 150 deg. cent., then decreases to a minimum, and at still
higher temperature increases to a second maximum, higher
than the first one, possibly between 600 and 800 deg. cent., and
then decreases again.
52. Essentially, however, the efficiency of light production
by the arc is a characteristic of the material of the arc stream,
and thus substances which give a large part of their radiation
as spectrum lines in the visible range — as calcium — give a
very efficient arc, while those substances which radiate most of
their energy as lines in the invisible, ultra-violet or ultra-red — -
as carbon — give a very inefficient arc. The problem of efficient
light production by the arc therefore consists in selecting such
materials which give most of their radiation in the visible range.
Carbon, which is most generally used for arc terminals, is
one of the most inefficient materials : the carbon arc gives very
little light, and that of a disagreeable violet color; it is practi-
cally non-luminous, and the light given by the carbon arc lamp
is essentially incandescent light, temperature radiation of the
incandescent tip of the positive carbon. The fairly high effi-
ciency of the carbon arc lamp is due to the very high tempera-
ture of the black body radiator, which gives the light.
LUMINESCENCE. 123
The materials which give the highest efficiencies of light
production by their spectrum in the arc stream arcs mercury,
calcium and titanium.
As mercury vapor is very poisonous, the mercury arc has to
be enclosed air-tight, and has been developed as a vacuum arc,
enclosed by a glass or quartz tube. Its color is bluish green.
Calcium gives an orange-yellow light of very high efficiency,
and is used in most of the so-called "flame-carbon arcs," or
"flame arcs."
Titanium gives a white light of extremely high efficiency.
It is used in the so-called "luminous arc," as the magnetite arc
in direct-current circuits, the titanium-carbide arc in alternating-
current circuits.
53. Two methods exist of feeding the light-giving material
into the arc stream :
(1) By electro-conduction, that is, using the material as the
vapor conductor which carries the current. In this case, it
must be used as negative, as the vapor conductor is supplied
from the negative; such arcs are called "luminous arcs."
(2) By heat evaporation; in this case, a very hot arc must be
used, and thus usually a carbon arc is employed. As the posi-
tive terminal is the hottest, the material is mixed with the car-
bon of the positive terminal, and as negative terminal either a
plain carbon, or also an impregnated carbon used; such arcs
are called "flame arcs."
The method of heat evaporation is always used witri calcium,
since no stable conducting calcium compound is known which
may be used as negative arc terminal. With titanium, usually
electro-conduction is employed, that is, a titanium oxide-mag-
netite mixture, or titanium carbide, used as negative terminal,
and any other terminal, as copper or carbon, as positive ter-
minal. Titanium can also be introduced by heat evaporation
by using a titanium-carbon mixture as positive terminal or as
both terminals of the flame-carbon arc.
Both methods of feeding — electro-conduction and heat evapo-
ration — have advantages and disadvantages.
Electro-conduction has the great advantage that the tem-
perature of the terminals is immaterial, as heat plays no part in
feeding the luminescent material into the arc flame. The posi-
tive terminal of the arc can be made sufficiently large and of
124 RADIATION, LIGHT, AND ILLUMINATION.
such material as not to consume at all, and the trimming of the
lamp thus reduced to the replacing of one electrode only — the
negative. The negative electrode also can be made so large as
to remain fairly cold, and therefore consumes only at the very
slow rate required to supply the arc vapor, but does not con-
sume by combustion or heat evaporation. Thus its rate of con-
sumption can be reduced to 1 mm. or less per hour (while the
open carbon arc of old consumes about 5 cm. of electrodes per
hour), and thereby even with a moderate size of electrode a life
of electrodes of 100 to 200 hr. or even much more secured. This
method of feeding thus lends itself very well to long-burning arcs,
as they are almost exclusively used for American street lighting.
By electro-conduction higher efficiencies can be reached than
by heat evaporation, as the arc vapor stream when produced by
electro-conduction can be made to consist entirely of the vapor
of the luminescent material, as when using metallic titanium as
negative terminal.
A disadvantage of the method of feeding the arc by electro-
conduction is the much greater limitation in the choice of
materials: the material must be an electric conductor, which is
stable in the air, and reasonably incombustible. In the method
of feeding by heat evaporation any material can be used, as
it is mixed with carbon, and the conductivity is given by the
carbon. Thus, in the titanium arc, either metallic titanium or
titanium carbide or sub oxide must be used, but the most com-
mon titanium compound, Ti02, or rutile, is not directly suitable,
since it is a non-conductor. In the direct-current titanium arc,
the so-called magnetite arc, a solution of Ti02, or rutile, in mag-
netite, Fe304, which is conducting, is used, that is, a mixture of
rutile with a considerable weight of magnetite. While mag-
netite also gives a luminous arc, — the white iron spectrum, —
the efficiency of the iron arc is lower than that of the titanium
arc, and the efficiency of the magnetite arc thus lower than that
of the pure titanium arc, though much higher than that of the
carbon arc.
Calcium cannot be used at all by electro-conduction: the
only more common conducting calcium compound is calcium
carbide. As negative terminal calcium carbide gives an arc of
an efficiency far superior to that of the flame-carbon arc, but,
as calcium carbide disintegrates in the air, it cannot be used.
LUMINESCENCE. 125
Still greater is the limitation for alternating current; in this
case the material, in addition to its other qualifications, must
have such a high boiling point as to maintain a steady alternat-
ing arc, as discussed above. Of the titanium compounds only
titanium carbide seems to fulfill this requirement; of the iron
compounds, apparently none.
54. The most serious disadvantage of the use of electro-
conduction for feeding the arc, however, has been the inherently
greater unsteadiness of metal arcs compared with the carbon
arc. It is this feature which has retarded the development
of true luminous arcs until recent years, that is, until means
were found to produce steadiness by eliminating the nickering
of the negative spot by the admixture of a more refractory
material, — chromite in the magnetite arc, — and eliminating
the unsteadiness due to the occasional momentary fading out
of the luminous inner core of the arc by the admixture of a very
small amount of some more volatile material.
The great advantage of the method of feeding the luminescent
material into the arc flame by heat evaporation, mainly from the
positive, is the possibility of using carbon as arc conductor,
which gives the inherent steadiness of the carbon arc, and thus
has led to the development of this type of high efficiency arc,
the flame arc, before the development of true luminous arcs.
A further advantage is the possibility of using alternating
current equally well and with the same electrodes as used with
direct current, as the arc is a carbon arc and thus operative on
alternating current
Another advantage is the great choice of materials available,
since practically any stable compound, whether conducting or
not, can be used in the flame carbon. Thus in the yellow-flame
arc, calcium fluoride, oxide and borates are used; in the tita-
nium arc, the oxide (rutile) or the carbide may be used.
The most serious disadvantage of the method of feeding by
heat evaporation, which has so far excluded the flame arc from
general use for American street illumination, is the rapid con-
sumption of the electrodes and their consequent short life.
Since the luminescent material is fed into the arc by heat evap-
oration, the electrodes must be so small that their ends are raised
to arc temperature, and thus rapidly consume by the combus-
tion of the carbon. The combustion cannot be reduced by
126 RADIATION, LIGHT, AND ILLUMINATION.
excluding the air by enclosing the arc with an almost air-tight
globe, as in the enclosed carbon arc, since the luminescent
material leaves the arc as smoke, and by depositing on the
globe rapidly obstructs the light. The rate of consumption of
the electrodes thus is the same as in the open carbon arc, 3 to
5 cm. (1 to 2 in.) per hour, and the flame-carbon arc even with
very great length of carbon thus lasts only one night, that is,
requires daily trimming. To some extent this difficulty may
be reduced by using the same air again, after passing it through
a smoke-depositing chamber in a so-called " circulating" or
"regenerative" flame lamp.
The mercury arc, being enclosed in a glass tube, necessarily
must always be fed by electro-conduction from the negative.
The calcium arc is always fed by heat evaporation from the
carbon positive, with a carbon negative, or from positive and
negative, by using flame carbons for both electrodes. The
titanium arc is usually fed by electro-conduction from the neg-
ative, but also by heat evaporation from the positive by using
a titanium-flame carbon.
55. As, by electro-luminescence, electric energy is converted
more directly into radiation, without heat as intermediary form
of energy, no theoretical limit can be seen to the possible effi-
ciency of light production by the arc, and in the mercury, cal-
cium and titanium arcs, efficiencies have been reached far beyond
those possible with temperature radiation. Thus, specific con-
sumptions of 0.25 watt per mean spherical candle power are
quite common with powerful titanium or calcium arcs, and even
much better values have been observed. It is therefore in this
direction that a radical advance in the efficiency of light pro-
duction appears most probable. At present, the main disad-
vantage of light production by the arc is the necessity of an
operating mechanism, an arc lamp, which requires some atten-
tion, and thereby makes the arc a less convenient illuminant
than, for instance, the incandescent lamp, and especially the
limitation in the unit of light: the efficiency of the arc decreases
with decrease of power consumption, and, while the arc is very
efficient in units of hundreds or thousands of candle power, its
efficiency is much lower in smaller units, and very small units
cannot be produced at all. Thus, for instance, while a 500-
watt flame arc may give 10 times as much light as a 500-watt
LUMINESCENCE. 127
carbon arc, to produce by a flame arc the same amount of light
as given by a 500-watt carbon arc requires very much more than
one-tenth the power. So far no way can be seen of maintaining
the efficiency of the arc down to such small units of light as
represented by the 16- or 20-eandle power incandescent lamp.
LECTURE VII.
FLAMES AS ILLUMINANTS.
56. Two main classes of illuminants exist: those producing
radiation by the conversion of the chemical energy of com-
bustion— the flames — and those deriving the energy of radia-
tion from electric energy — the incandescent lamp and the arc
lamp, and other less frequently used electric illuminants.
Flames.
To produce light from the chemical energy of combustion,
almost exclusively hydrocarbon flames are used, as the gas flame,
the candle, the oil lamp, the gasolene and kerosene lamp, etc.;
that is, compounds of hydrogen and carbon or of hydrogen,
carbon and some oxygen are burned. The hydrogen, H, com-
bines with the oxygen, 0, of the air to water vapor, H20, and the
carbon, C, with the oxygen of the air, to carbon dioxide, C02;
or, if the air supply is insufficient, to carbon monoxide, CO, a
very poisonous, combustible, odorless gas (coal gas), which
thus appears in all incomplete combustions and is present, also,
as intermediary stage, in complete combustion.
The mechanism of the light production by the hydrocarbon
flame I illustrate here on the luminous gas flame : where the gas
issues from the burner into the air, it burns at the surface of the
gas jet. By the heat of combustion the gas is raised to a high
temperature. Most hydrocarbons, however, cannot stand high
temperatures, but split up, dissociate into simpler hydro-
carbons very rich in hydrogen : methane, CH4, and in free carbon.
The carbon particles formed by this dissociation of hydrocar-
bon gas float in the burning gases, that is, in the flame, and are
raised to a high temperature by the heat of combustion of the
gases, thereby made incandescent, and radiate light by tem-
perature radiation; until ultimately, at the outer edge of the
flame, they are burned by the oxygen of the air, and thus
destroyed. We can see these carbon particles, which, floating
128
FLAMES AS ILLUMINANTS. 129
in the flame in anjncandescent state, give the light if, by passing
a cold porcelain or glass plate through the luminous flame,
we suddenly chill it and thereby preserve the carbon particles
from combustion; they appear then on the plate as a carbon
deposit, soot or lampblack. The light given by the luminous
hydrocarbon flame thus is due to black-body radiation, and the
flame makes its own radiator, and afterwards destroys it by
combustion.
To give a luminous flame, the hydrocarbon must be suffi-
ciently rich in carbon to split off carbon at high temperatures.
Thus methane, CH4, does not give a luminous flame, since it con-
tains the smallest amount of carbon which can combine with
hydrogen, and therefore does not deposit carbon at high tem-
peratures. Ethylene, however, C2H4, which is the foremost
light giving constituent of illuminating gas, dissociates in the
flame into CH4 and C, and thus gives a luminous flame, as half
of its carbon is set free and gives the incandescent radiator.
If, however, the hydrocarbon is very rich in carbon, the
amount of deposited carbon becomes so large that the energy
of combustion of the remaining hydrocarbon is not sufficient to
raise the carbon to very high temperatures, the luminosity
therefore again decreases, the flame becomes reddish yellow,
and a large amount of carbon escapes from the flame uncon-
sumed, as smoke or soot, that is, the flame becomes smoky.
To show you this, I pour some gasolene and some benzol in
small glass dishes. The gasolene, having 2J hydrogen atoms
per carbon atom, burns with a luminous flame and very little
smoke. The benzol, having only one hydrogen atom per carbon
atom, burns with a reddish-yellow flame, pouring out masses
of black smoke.
The proportion between the hydrogen and carbon required
to give a luminous non-smoky flame, therefore can be varied
only within narrow limits: too little carbon gives a less lumi-
nous or non-luminous flame, too much carbon a smoky reddish
flame.
Hydrocarbons exist having almost any proportion between
hydrogen and carbon, from a maximum of four hydrogen atoms
to one carbon in methane, CH4, to practically pure carbon in
anthracite coal. Some of them are shown in the following
table, with the number of hydrogen atoms per carbon atom
130
RADIATION, LIGHT, AND ILLUMINATION.
added in column a, and the percentage of carbon which is de-
posited by dissociation, in column b ;* a thus may be called the
luminosity index of the hydrocarbon.
HYDROCARBONS.
Name.
State.
Formula.
Lumi-
nosity
Index
(a).
Car-
bon
Index
(ft).
Paraffines:
Methane
Gas.
do..
CH4
C2H6
C3H8
r4H10
^5n!2
C«H14
C10H22
^14^30
C20H42
U24±150
C2H4
C2H2
C.H6
C10H8
C14H10
approx.
4.0
3.0
2.67
2.5
2.4
2.33
2.2
2.14
2.1
2.08
2
1
1
0.8
0.71
0
0.25
0.333
0.375
0.40
0.417
0.45
0.464
0.475
0.479
0.50
0.75
0.75
0.80
0.821
Ethane
Propane
. do...
Butane
. . do...
Pentane . ...
Liquid.
..do..
. . .do....
Gasolene
Kerosene
Mineral oil
Vaseline
.. .do....
Solid,
do
Paraffine
Olefines:
Ethylene
Gas.
Gas.
Liquid.
Solid,
do..
Acetylenes:
Acetylene
Benzols:
Benzol
Naphthalene
Anthracene
57. The proportion between carbon and hydrogen required to
give a luminous non-smoky flame somewhat depends on the
size of the flame, and, with a larger size, a higher proportion of
hydrogen is required to avoid smoke than with a smaller flame,
as in the latter, due to the larger surface compared with the
volume, the combustion is more rapid. I show you this on the,
gas flame : admitting a little gas, I get a small flame, which does
not smoke, but if I open the stop-cock wide I get a large and
smoky flame.
With a moderate-sized flame without artificial ventilation,
from 30 to 40 per cent of the carbon must be deposited to give
good luminosity without smoke. This corresponds to a value a
* Every four hydrogen atoms retain one carbon atom, while the rest of the
carbon is set free.
FLAMES AS ILLUMINANTS. 131
between 2.4 and somewhat less than three hydrogen atoms per
carbon atom. Ethane, C2H6, with a = 3, still gives a luminous
flame, but of somewhat lower luminosity, and, on the other
side, the gasolene flame, a = 2.33, is slightly smoky. However,
in very small flames in which the surface is larger compared
with the volume, and the combustion thus very rapid, higher
percentages of carbon can be used without smoke. Thus the
flame of the parafnne candle a = 2.08 is still smokeless but
begins to smoke if it gets large, and in extremely small flames,
J in. or less diameter, even acetylene, a = 1, gives smokeless
combustion.
Increase of the rapidity of combustion by increasing the sur-
face of the flame by using a flat or hollow cylindrical burner,
and increasing the air supply by artificial draft, as by a chimney,
gives smokeless flames even up to b = 50, or one carbon atom
to two hydrocarbon atoms, a = 2.
Thus kerosene, which, due to its high carbon content a = 2.14,
smokes badly, except in very small flames, is burned smoke-
lessly in lamps with chimneys and flat or hollow round burners,
and then gives a high light intensity : with the rapid air supply
and the large surface of the thin flame, the combustion is very
rapid, a part of the free carbon is immediately consumed, the
temperature is high, and thus the free carbon heated sufficiently
to give considerable light, and to consume completely when
leaving the flame. With a hydrocarbon still richer in carbon,
as acetylene or benzol a = 1, artificial draft and large flame
surface are no longer sufficient to give smokelessness, and the
total range of hydrocarbons which can be burned with lumi-
nous flames and without smoke thus is between from three to
two hydrogen atoms per carbon atom.
Hydrocarbons which are too rich in carbon to be burned
smokelessly, as acetylene or benzol, obviously can be burned
with a smokeless luminous flame by mixing them in the proper
proportions with hydrocarbons deficient in carbon, which latter
by themselves would give a non-luminous or nearly non-lumi-
nous flame. Thus a mixture of one volume of acetylene, C2H2,
with three volumes of methane, 3 CH4, (the number of mole-
cules of gases are proportional to their volumes), gives a non-
smoky luminous flame: 5 C to 14 H, or a = 2.8.
Such hydrocarbons as acetylene, benzol, etc., which are rich
132 RADIATION, LIGHT, AND ILLUMINATION.
in carbon, are used for enriching poor gas, that is, making it
more luminous : gas which gives little free carbon, as water-gas
(which is rich in H and CO — both giving non-luminous flames),
and which therefore would give a non-luminous or only slightly
luminous flame, thus is improved in its light-giving quality
by admixture of acetylene, etc.
58. If the hydrocarbon contains oxygen, as alcohol, C2H60,
etc., the presence of oxygen atoms reduces the luminosity or
the tendency to smoke, by taking care of a corresponding num-
ber of carbon atoms: the most stable compound is CO, and
water vapor, H20, as well as carbon dioxide, C02, are reduced
by carbon at high temperature with the formation of carbon
monoxide, CO. During the dissociation of the hydrocarbon in
the flame, each oxygen atom takes up one carbon atom, form-
ing CO, which burns with a non-luminous flame. In approxi-
mately estimating the luminosity or the tendency to smoke of a
hydrocarbon containing oxygen, for each oxygen atom one car-
bon atom is to be subtracted. To illustrate this I pour some
aldehyde, C2H40, and some amyl acetate, C7H1402, in small glass
dishes and ignite them. In both the ratio of hydrogen to car-
bon atom is a = 2, corresponding to a luminous but smoky
flame. You see, however, that the aldehyde burns with a per-
fectly non-luminous flame : we have to put out the light to see
it; while the amyl acetate burns with a luminous, non-smoky
flame. Applying above reasoning, the oxygen accounts for one
carbon atom in the aldehyde : C2H40 = CO + CH4, and in CH4 :
a = 4, corresponding to a non-luminous flame, as observed. In
amyl acetate, the two oxygen atoms take up two carbon atoms :
C7H1402 = 2 CO + C5H14, and the ratio of hydrogen to carbon
atoms is a = 2.8, or b = 30, corresponding to a luminous non-
smoky flame, as observed.
The same effect as given by oxygen contained in the hydro-
carbon molecule obviously is obtained by mixing oxygen or
air with the hydrocarbon. I illustrate this on the bunsen
flame : closing the air supply, I have an ordinary luminous and
somewhat smoky gas flame. I now gradually admit air, and you
see first the smoke disappear, and then the luminosity decreases,
and first the lower part, and then the entire flame, becomes
non-luminous. When the luminosity has just disappeared, the
amount of air mixed with the gas is just sufficient to take up
FLAMES AS ILLUMINANTS. 133
all the carbon as CO, which would deposit otherwise and give
the incandescent radiator, but it is far below the amount required
for complete combustion, and, by still further increasing the air
supply, you see the rapidity of combustion still further increase,
as shown by the decreasing size of the flame. With increasing
air supply, the size of the flame very greatly decreases, and, as
the same total heat is produced by the combustion, this means
that the heat is concentrated. in a smaller volume, that is, the
temperature of the flame is increased, in other words, the non-
luminous bunsen flame is of higher temperature than the lumi-
nous gas flame.
Hydrocarbons which are too rich in carbon to burn without
smoke, as acetylene, can be burned with a smokeless flame by
mixing them with oxygen or with air. Acetylene is always
burned in this manner, and all acetylene-gas burners are con-
structed so as to take in air with the acetylene gas before com-
bustion, that is, are small bunsen burners or similar thereto.
Since the temperature of the bunsen flame, due to the more
rapid combustion resulting from the mixture with air, is higher
than that of the ordinary gas flame, and in the acetylene flame
in the acetylene air mixture a large part of the carbon is also
immediately burned, the temperature of the acetylene flame is
very high, and the deposited carbon therefore raised to a very
high temperature, much higher than in the ordinary gas flame,
and, as the result of the higher temperature, the black-body
radiation of the free carbon in the acetylene flame is far more
efficient, and of much whiter color than in the ordinary gas flame.
Thus the hydrocarbons which are very rich in carbon, as
acetylene, benzol, naphthalene, etc., if burned smokelessly by
mixture with air, give whiter and more efficient flames, due
to their higher temperature. Especially is this the case with
acetylene, as the energy of combustion of acetylene is higher
than that of other hydrocarbons of the same relative propor-
tions of hydrogen and carbon: acetylene being endothermic,
that is, requiring energy for its formation from the elements.
59. Since, as discussed in Lecture VI, chemical luminescence
usually occurs where intense chemical reactions take place at high
temperatures, — and this is the case in the flame, — chemical
luminescence of the flame gases must be expected in the hydro-
carbon flame. It does occur, but does not contribute anything
134 RADIATION, LIGHT, AND ILLUMINATION.
to the light production, since the spectra of hydrogen and of
carbon (or CO and CH4) are practically non-luminous. The
luminescence of the hydrocarbon flame therefore can be observed
only with those hydrocarbons which are sufficiently poor in car-
bon as not to deposit free carbon, as methane, alcohol, etc., or
in which, by the admixture of air, the deposition of free carbon
and thereby the formation of an incandescent radiator, is
avoided, as in the bunsen flame. In this case, the blue color of
the chemical luminescence of carbon-flame gases is seen: all
non-luminous hydrocarbon flames are blue.
60. While light, and radiation in general, can also be pro-
duced by the combustion of other materials besides hydro-
carbons, industrially other materials are very little used.
Burning magnesium gives a luminous flame of extremely
high brilliancy and whiteness. Its light is largely due to tem-
perature radiation, and the flame makes its own incandescent
radiator; but unlike the hydrocarbon flame, in which the radiator
is again destroyed by combustion, the incandescent radiator of
the magnesium flame is the product of combustion, magnesia,
MgO, and escapes from the flame as white smoke. While, how-
ever, in the hydrocarbon flame the incandescent radiator is a
black body, — carbon, — giving the normal temperature radiation,
the radiator of the magnesium flame, magnesia, is a colored
radiator, and its radiation is deficient in intensity in the ultra-
red, and very high in the visible range, and thereby of a much
higher efficiency than given by black-body radiation. The
magnesium flame therefore is far more efficient than the hydro-
carbon flame, and its light whiter.
So also burning aluminum, zinc, phosphorus, etc., give lu-
minous flames containing incandescent radiators produced by
the combustion: alumina, zinc oxide, etc.
Superimposed upon the temperature radiation of the incan-
descent radiator of those flames is the radiation of chemical
luminescence. Since, however, magnesium, zinc, aluminum,
give fairly luminous spectra, in these flames the chemical lumi-
nescence contributes a considerable part of the light, and where
the luminescent light, that is, the metal spectrum, is of a marked
color — as green with zinc — the flame of the burning metal
also is colored. Hence burning zinc gives a greenish-yellow
flame, burning calcium an orange -yellow flame, etc.
FLAMES AS ILLUMINANTS. 135
Obviously, where during the combustion no solid body is
formed, the light given by the flame is entirely chemical lumi-
nescence. Thus burning sulphur gives a blue flame, and, if
the temperature of combustion is increased by burning the
sulphur in oxygen, it gives a fairly intense light, of violet color,
and a radiation which is very intense in the ultra-violet. Thus
before development of the ultra-violet electric arcs, as the iron
arc, for the production of ultra-violet radiation lamps were used,
burning carbon bisulphide, CS2, in oxygen. Carbon bisulphide,
has the advantage over sulphur that, as liquid, it can easier be
handled in a lamp, and especially the combustion of carbon
(without adding much to the light, due to the non-luminous
character of the carbon spectrum) greatly increases the flame
temperature, and thereby the intensity of the radiation.
Flames with Separate Radiator.
61. The hydrocarbons are the only sources of chemical
energy which by their cheapness are available for general use
in light production. Carbon, however, is a black-body radiator,
and its efficiency of light production therefore very low, es-
pecially at the relatively low temperature of the luminous
hydrocarbon flame, and such flames are, therefore, low in
efficiency of light production, with the exception of the acety-
lene flame and other similar flames.
Separating the conversion into light from the heat production;
that is, using the hydrocarbon flame merely for producing heat,
and using a separate radiator for converting the heat into light,
offers the great advantage
(1) That a colored body can be used as radiator, and thereby
a higher efficiency of light production, at the same temperature,
secured, by selecting a body deficient in invisible and thereby
useless radiation.
(2) That the rapidity of combustion can be greatly increased
by mixing the hydrocarbon with air in a bunsen burner, and
thereby the temperature of the flame increased, which results
in a further increase of the efficiency of light production.
Thus, by the use of suitable external radiators, in a non-
luminous hydrocarbon flame, far higher efficiencies of light
production are reached than by the use of the luminous hydro-
carbon flame.
136 RADIATION, LIGHT, AND ILLUMINATION.
The first use of external radiators probably was the use of a
lime cylinder in a hydro-oxygen flame, in the so-called "lime
light/' for producing very large units of light. in the days before
the electric arc was generally available.
In the last quarter of a century the external radiator has
come into extended use in the Welsbach mantle; the hydro-
carbon is burned in a bunsen burner, that is, mixed with air, so
as to get a non-luminous flame of the highest temperature, and
in this flame is immersed a cone-shaped web of a highly effi-
cient colored radiator: thoria with a small percentage of ceria,
etc., the so-called "mantle." The higher temperature, com-
bined with the deficiency of radiation in the invisible range, ex-
hibited by this colored radiator, results in an efficiency of light
production several times as high as that of the luminous gas
flame. The distribution of intensity in the spectrum of the
Welsbach mantle obviously is not that of black-body radiation,
but differs therefrom slightly, and the radiation is somewhat
more intense in the greenish yellow, that is, the light has a
slightly greenish-yellow hue.
The Welsbach mantle is very interesting as representing the
only, very extensive industrial application of colored radiation.
LECTURE VIII.
ARC LAMPS AND ARC LIGHTING.
Volt- Ampere Characteristics of the Arc.
62. The voltage consumed by an arc, at constant current,
increases with increase of arc length, and very closely propor-
tional thereto. Plotting the arc voltage, e, as function of the
190
180
170
160
150
140
130
120
110
100
00
80
70
60
50
'40
30
20
10
I.fi6
0[5
25
1 0
FIG. 45.
arc length, I, we get tor every value of current, i, a practically
straight line, as shown for the magnetite arc in Fig. 45, for values
of current of 1, 2, 4 and 8 amperes. These lines are steeper
137
138
RADIATION, LIGHT, AND ILLUMINATION.
for smaller currents, that is, low-current arcs consume a higher
voltage for the same length than high-current arcs, the in-
crease being greater the longer the arc. These lines in Fig. 45
intersect in a point which lies at I = — 0.125 cm. = — 0.05 in.
and e = 30 volts; that is, the voltage consumed by the arc
consists of a part, e0 = 30 (for the magnetite arc), which is con-
F;G. 46.
stant, that is, independent of the arc length and of the cur-
rent in the arc, but different for different materials, and a
part, ev which is proportional to the arc length, Z, or rather to
the arc length plus a small quantity, 1L= 0.125 (for the magne-
tite arc): e^ = \(l + 0.125), and depends upon the current,
being the larger the smaller the current.
Plotting the arc voltage, e, as function of the current, i, we
get curves which increase with decrease of current, the increase
being greater the longer the arc, as shown in Fig. 46, for the
ARC LAMPS AND ARC LIGHTING. 139
magnetite arc, for I = 0.3, 1.25, 2.5, 3.75 cm. = 0.125, 0.5, 1 and
1.5 in. Subtracting from the voltage, 6, in Fig. 46, the con-
stant part, e0 = 30 volts, which apparently represents the
terminal drop of voltage, that is, the voltage which supplies
the energy used in producing the conducting vapor stream
at the negative, and the heat at the positive terminal, leaves
the voltage, el = e — eQJ as the voltage consumed in the arc
stream.
The curves of arc-stream voltage, ev as function of the cur-
rent, ij in Fig. 46, can with approximation be expressed by
k
cubic hyperbolas: e^i = kz2; or, el =— £j and since we find for
Vi
constant value of current: el = k^ (I + 0.12), as function of
arc length and current, i, the voltage of the arc stream is ex-
pressed by : k (I + I)
ei = TT1-' (1
and the total arc voltage by :
, *(*+*,:
(2)
where e0, k and Zt are constants of the terminal material (k, how-
ever, varies with the gas pressure in the space in which the arc
exists).
This equation (2) represents the arc characteristics with
good approximation, except for long low-current arcs, which
usually require a higher voltage than calculated, as might be
expected from the unsteady nature of such long thin arcs.
The equation (2) can be derived from theoretical reasoning
as follows: Assuming the amount of arc vapor, that is, the
volume of the conducting vapor stream, as proportional to the
current, and the heat produced at the positive terminal also as
proportional to the current, the power p0 required to produce
the vapor stream and the heating of the positive terminal is
proportional to the current, i\ and, as the power is p0 = eQi, it
follows that the voltage, e0, consumed at the arc terminals is
constant.
The power consumed in the arc stream : pl = ej,, is given off,
by heat conduction, convection, and by radiation, from the sur-
140 RADIATION, LIGHT, AND ILLUMINATION.
face of the arc stream, and thus, as the temperature of the arc
stream is constant, and is that of the boiling point of the arc
vapor, the power pl consumed in the arc stream is proportional
to its surface, that is, to the product of arc diameter ld and arc
length I, or rather the arc length I increases by a small quantity
lv which allows for the heat carried away to the electrodes. As
the diameter ld is proportional to the square root of the section
of the arc stream, and the section of the arc stream, or the
volume of the arc vapor, was assumed as proportional to the
current, i, the arc diameter is proportional to the square root
of the current, and the power pt consumed in the arc stream thus
is proportional to the square root of the current, i, and to (I + IJ ;
thatis' p^kVid + lJ;
and since pl = ej,
which is equation (1), and herefrom, since e = e0 + eir follows
equation (2).
63. Since e0 represents the power consumed in producing the
vapor stream and the heating of the positive terminal, and k
the power dissipated from the arc stream, e0 and k are different
for different materials, and in general higher for materials of
higher boiling point and thus higher arc temperatures. It is,
approximately,
e0 = 13 volts for mercury,
= 16 volts for zinc and cadmium,
= 30 volts for magnetite,
= 36 volts for carbon,
k = 31 for magnetite (123 in inch measure),
= 35 for carbon (130 in inch measure).
The magnetite arc, of which the characteristics are shown in
Figs. 45 and 46, thus can be represented by:
' (3)
The least agreement with the theoretical curve (2) is shown by
the carbon arc. This may be expected from the exceptional
character of the carbon arc, as discussed in Lecture VI. Plot-
ARC LAMPS AND ARC LIGHTING.
141
ting, in Fig. 47, the voltage, e, consumed by a carbon arc, at
constant values of current i, as function of the arc length Z, —
as done for the magnetite arc in Fig. 45, — when using only the
observation for arc length of 0.25 in. and over, we get fairly
satisfactory straight lines, which intersect at the point, giving
e0 = 36 volts, but I, = - 0.8 cm. = - 0.33 in.; that is, a
value much greater than for any other arc. For short arc
VOLTS
150-
•100
2
LE
-20-
25
3 "5 cn
1J5 IN.
FIG. 47.
lengths, however, the observed values of voltage drop below
the straight line, as shown in Fig. 47, and converge towards a
point, at zero arc length, or e0' = 28 volts. This looks as if, of
the potential drop of e0 = 36 volts of the carbon arc, only a
part, e0' = 28 volts, occurs at the surface of the terminals, and
the remaining part, e" = 8 volts, occurs in the space within
a short distance from the terminal surface. If then the arc
length is decreased to less than the distance within which the
terminal drop e" occurs, the arc meets only a part of this ter-
minal drop e", and, for very short arc length, only the terminal
drop e0' occurs. Possibly the voltage e0' = 28 is consumed at
the negative terminal in producing the conducting vapor stream,
142 RADIATION, LIGHT, AND ILLUMINATION.
while the voltage e" = 8 is consumed by the moving vapor
stream in penetrating a layer of dead carbon vapor formed by
heat evaporation from the positive terminal, and surrounding
this terminal.
Stability Curves of the Arc.
64. From the volt-ampere characteristic of the arc, as rep-
resented by equation (2) and reproduced in Fig. 48 as Curve I,
for a magnetite arc of 1.8 cm. (about 0.75 in.) length, it follows
that the arc is unstable on constant potential supply, as the,
voltage consumed by the arc decreases with increase of current
and, inversely, a momentary increase of current decreases the
consumed voltage, and, on constant voltage supply, thereby
increases the current, still further decreases the arc voltage
and increases the current, and the arc thus short circuits; or a
momentary decrease of current increases the required voltage
and, at constant supply voltage, continues to decrease the cur-
rent and thus increase still further the required voltage, that is,
the arc goes out.
On constant voltage supply only such apparatus can operate
under stable conditions in which an increase of current requires
an increase, and a decrease of current a decrease of voltage,
and thus checks itself.
Inserting in series with the arc, curve I, in Fig. 48, a constant
resistance of 10 ohms, the voltage consumed by this resistance,
e = ir, is proportional to the current, and given by the straight
line II. Adding this voltage to the arc voltage curve I, gives
the total voltage consumed by the arc and its series resistance,
as curve III. In curve III, the voltage decreases with increase
of current, for values of current below i0 = 2.9 amperes, and the
arc thus is unstable for these low currents, while for values of
current larger than i0 = 2.9 amperes, the voltage increases with
increase of current. The point i0 = 2.9 amperes thus separates
the unstable lower part of the curve III from the stable upper
part. With a series resistance of r = 10 ohms, a 1.8-cm. mag-
netite arc thus requires at least e = 117 volts supply voltage,
and i0 = 2.9 amperes for steady operation. With a larger
series resistance, as r = 20 ohms, represented by curve II' and
III', a larger supply voltage is required, but smaller currents can
be operated ; with a lower series resistance, r = 5 ohms, curves
ARC LAMPS AND ARC LIGHTING.
143
II" and III", larger currents are required for stable operation,
but a lower supply voltage is sufficient.
When attempting to operate an arc close to the stability limit,
i0, where a small variation of voltage causes a large variation of
current, the operation of the arc is unsatisfactory, that is, the
FIG.
current drifts; small variations of the resistance of the arc
stream, and thereby of the voltage consumed by the arc, cause
excessive fluctuations of the current. These pulsations of cur-
rent can be essentially reduced by using a large inductance
in series with the arc, and an arc can be operated very much
closer to its stability limit if its series resistance is constructed
highly inductive, that is, wound on an iron core. Obviously,
144 RADIATION, LIGHT, AND ILLUMINATION.
no series inductance can extend stable operation beyond the
stability point %.
At the stability limit iQJ the resultant characteristic III in
Fig. 48 is horizontal, that is, the slope of the resistance curve
ef
II, r = - i is equal but opposite to the slope of the arc char-
de
acteristic I, — ; that is, at the stability limit,
ii+r=°-> ; <*>
and, substituting equation (2) in (4), gives
and the total voltage consumed by the arc of current i and
length I and the series resistance r required to just reach sta-
bility is
E = e + ir,
, fe (* + Z.) , * (Z + Z.) .
— eo ~r - — ; r - — 7: — ,
\/i 2 Vt
that is,
/. VTV
or, E^e+ti. (6)
This curve is called the stability curve of the arc. It is shown
as IV in Fig. 48. It is of the same form as the arc characteristic
I, and derived therefrom by adding 50 per cent of the voltage
consumed in the arc stream.
Thus, in an arc requiring 80 volts, of which e0 = 30 volts are
consumed at the terminals, ^ = 50 volts in the arc stream,
for stable operation, a supply voltage of more than E = e + -^
= 80 + 25 = 105 volts is required.
ARC LAMPS AND ARC LIGHTING. 145
The stability limit, on constant potential, thus lies at an ex-
cess of the supply voltage over the arc voltage by 50 per cent of
the voltage, ev consumed in the arc stream. In general, to get
reasonable steadiness of the current, and absence of drifting, a
supply voltage is used which exceeds the arc voltage by from
75 per cent to 100 per cent or more of the voltage, ev of the arc
stream.
65. The preceding consideration applies only to those arcs
in which the gas pressure in the space surrounding the arc, and
thereby the arc vapor pressure and temperature, are constant
and independent of the current, as is the case with arcs in air
(even " enclosed" arcs, as the enclosure cannot be absolutely air-
tight), as it is based on the assumption that the section of the
vapor stream is proportional to the current. With arcs in
which the vapor pressure and temperature vary with the current,
as with vacuum arcs, as the mercury arc, the reasoning has to be
correspondingly modified. Thus in the mercury arc in a glass
tube, if the current is sufficiently large to fill the entire tube, and
not so large that condensation of the mercury vapor cannot
freely occur in the condensing chamber, the power pl dissi-
pated by radiation, etc., may be assumed as proportional to the
length Z of the tube, and to the current i:
pi = 6li = kli, (7)
thus gives e1 = klf or independent of the current; and
e = e0 + ev
= e0 + A*; (8)
that is, the voltage consumed by a mercury arc, within a cer-
tain range of current, is constant and independent of the cur-
rent, and consists of a constant part, the terminal drop e0, and
a part which is proportional to the length and to the diameter
of the tube.
Approximately it is for the mercury arc in a vacuum:
1.4
e0 = 13 volts ; k = -y-
Id
hence, ,
Calculating approximately the increase of vapor pressure and
thereby of arc-stream resistance at high currents, and the
146 RADIATION, LIGHT, AND ILLUMINATION.
increase of resistance at low current, due to the arc stream not
completely rilling the vapor tube, gives for the vacuum arc the
approximate equation:
I
e = e« + df°>
7 7 • d
ald -01 r-
^
where
ld = diameter of arc tube, cm.,
I = length of arc, cm.,
i = current.
For the mercury arc, it is :
e0 = 13 volts,
a = 1.68,
6 = 0.29 for mercury anode,
= 0.167 for graphite or metal anode,
c = 0.52.
Arc Length and Efficiency.
66. The arc most frequently employed for illumination is
the plain carbon arc. In this the arc flame of the vapor stream
gives no useful light, but the light is given by the black-body
radiation of the incandescent carbon terminal, mainly the
positive terminal, which is hottest, and is given at high efficiency
due to the very high temperature of the radiator. The light
of the carbon arc thus is incandescent light, and not lumines-
cence. In the alternating carbon arc, alternately, the two ter-
minals are positive and negative, and, as relatively little heat is
produced at the negative terminal, the average temperature of
the carbon terminals of an alternating arc is lower, and the
efficiency of light production therefore less. Thus, while direct-
current carbon arcs reach efficiencies corresponding to specific
consumptions of from 1 to 1.5 watts per mean spherical candle
power, alternating carbon arcs show only from 2.5 to 3 watts
per candle power, or even still higher specific consumption.
Thus, the only excuse for the use of the alternating carbon arc
is the much greater simplicity and convenience of the electric
generating apparatus, the stationary transformer, compared to
the arc machine with the direct-current arc, and with the de-
velopment of the constant-current mercury-arc rectifier; this
ARC LAMPS AND ARC LIGHTING.
147
difference in the simplicity of generation of the arc current has
largely disappeared.
In the direct-current carbon arc, the light comes mainly from
the positive terminal; in the alternating carbon arc equally
from both terminals, and the distribution curve of the light
thus is different.
Since in the carbon arc no useful light comes from the arc
flame, the voltage and therefore the power consumed in the
arc flame is wasted, and in general, therefore, the efficiency of
light production of the carbon arc is the higher the shorter the
arc. Thus comparing in Fig. 49 a 1-in. carbon arc A with a
FIG. 49.
0.5-in. carbon arc B, the former requires, at 5 amperes, 112
volts and 560 watts, the latter only 84 volts and 420 watts,
but radiates the same amount of light from the incandescent
tip of the positive carbon. As the 1-in. arc requires 33 per
cent more power, and only produces the same amount of light,
it is less efficient than the latter. Thus, the shorter we make
the arc and the less power we therefore consume in it the more
efficient seems the light production, as we produce the same
amount of light radiation from the positive terminal in either
case. When we come to short arc lengths, however, while the
same amount of light is produced at the positive terminal, we
do not get the same amount of light from the lamp, as an
increasing part of the light is intercepted by the negative ter-
minal. Thus with the 1-in. arc, A, in Fig. 49, the light escapes
148 RADIATION, LIGHT, AND ILLUMINATION.
freely from the incandescent positive only in the space above
the lines m, while at m the shadow of the negative terminal
begins to obstruct the light more and more, and does so com-
pletely vertically below the arc. In the 0.5-in. arc B the area
covered by the shadow of the negative terminals is somewhat
increased, but in both arcs A and B the obstruction of the
light by the shadow of the negative is still so small that the
saving in power far more than makes up for it. In the 0.125-in.
arc, however, C in Fig. 49, the shadow of the negative ter-
minal m has crept up greatly, and thus, when decreasing the
arc length, a point is reached where the increasing shadow
of the negative terminal reduces the light more than the de-
creasing arc length reduces the power supply. Maximum
efficiency of light production thus is reached in the carbon arc
at a certain definite arc length (which depends on the size of
the electrodes and on the current), at which the change of
power consumption just balances the change of radiated light,
which results from a change of arc length and thereby of
shadow of negative terminal.
With the high-current (9 to 10 amperes) open arcs, the maxi-
mum efficiency point is at about J-in. arc length, giving a
voltage consumption of about 45 to 50 volts. Such arcs require
daily trimming, and therefore are no longer used in American
cities, except in a few places.
The open or short-burning arc has been practically entirely
superseded by the enclosed or long-burning arc lamp, in which
the arc is enclosed by an almost air-tight globe, the combustion
of carbon is greatly decreased, and the life of the carbons thus
increased about tenfold.
In the open arc of large current, the carbon terminals burn
off into a rounded shape, but in the enclosed arc, the current
being less and combustion greatly reduced, the carbon terminals
burn off to more flat shape, and thus obstruct the light more;
and, furthermore, since at the lower current the size of the
incandescent spot of the positive terminal is less, the maximum
efficiency of light production in the enclosed arc lamp is reached
at a much greater arc length, about f in. As the result
thereof, the enclosed arc lamp, with 5, 6.5 or 7.5 amperes in
the arc, consumes from 70 to 75 volts.
67. Entirely different are the conditions in the luminous
ARC LAMPS AND ARC LIGHTING. 149
arc, as the magnetite arc. In this, the light is given by the
vapor stream, and not by the terminals, and the voltage e0
and power consumed by the terminal drop thus is wasted, and
the voltage el and power pt consumed by the arc stream is
useful for light production. The greater, therefore, the voltage
el of the arc stream is, compared with the terminal drop e0, or in
other words the longer the arc, the higher is the efficiency of
light production. Thus a 4-amp. magnetite arc of 0.125-in.
length requires 41 volts, while a 0.5-in. 4-amp. arc requires 64
volts ; that is, only 56 per cent more voltage and thus power, but
gives about four times the light. A 1-in. arc requires 95 volts
or 48 per cent more power than the 0.5-in. arc, and gives twice
the light. The greater, thus, the arc length of the luminous
arc, with the same current, the higher is the efficiency. How-
ever, at the same current, the longer the arc, the greater is the
power consumption. In the design of the arc lamp the power
consumption is given, and the problem is to select the most
efficient arc length for a given and constant power consumption.
As an increase of arc length increases the arc voltage for the
same power consumption, the current has to be decreased, and
the efficiency of the arc conductor decreases with decrease of
current. Thus, with increasing arc length at constant power
consumption in the luminous arc, a point is reached where the
decrease of current required by the increase of arc length and
thus arc voltage decreases the efficiency more than the increase
of arc length increases it. Thus with the luminous arc, for
a given power consumption, a definite arc length exists, which
gives maximum efficiency.
Assuming the light given by the arc to be proportional to the
arc length and the current in the arc,
L = k'li, (9)
if the power p shall be consumed in the arc,
ei = p] (10)
however, by (2),
e=e0 + ^ (11)
Vi
(neglecting the small quantity lv as the calculation can obviously
be approximate only).
150 RADIATION, LIGHT, AND ILLUMINATION.
From (10) and (11) follows:
~ (12)
fe
and, substituting this in (9), gives:
k
L = - (pVi - ejVi), (13)
and the maximum amount of light produced by power p is
given by: dL
This gives
(14)
3e0
hence, by (13): 0 z,
(15)
and herefrom, by (12) and (11), the values of the arc length Z
and the arc voltage e.
Assuming p = 300 watts, and the constants of the magnetite
arc: eQ = 30, k = 31, gives:
i = 3.33 amperes,
e = 90 volts,
I = 2.21 cm. = 0.885 in.
Near the maximum efficiency, where the efficiency curve is
horizontal, the efficiency does not vary much for moderate
changes of current and of arc length. Thus, in above instance,
practically the same efficiency is reached for currents from 3
amperes to 4 amperes.
Larger currents and shorter arc lengths, however, are pref-
erable in an arc lamp.
(1) Because the shorter and thicker arc is less affected by
minor air currents, etc., than the thin long arc, hence, is steadier.
(2) The shorter arc gives lower voltage, and this, in constant-
current arc lighting, permits with the same total circuit voltage
the use of more arc lamps in series.
Thus in the magnetite arc lamp a current of 4 amp. has been
chosen.
i = 4: e = 75 volts, and I + l^ = 0.73 in., or about f-in. arc
length.
ARC LAMPS AND ARC LIGHTING. 151
In general, obviously the maximum efficiency points of lumi-
nous arcs occur at much greater arc lengths than in the plain
carbon arc.
Since the lower efficiency of the alternating carbon arc is due
to the lower temperature of the terminals, which are heated
during one half-wave only, and in the luminous arc the tem-
perature of the terminals does not determine the light pro-
duction, but the light is produced by the vapor stream, no
essential difference exists in the efficiency of a luminous arc,
and practically no difference in the efficiency of the flame-
carbon arc, whether operated on alternating or on direct current;
that is, the alternating luminous or flame-carbon arc, with the
same luminescent material, has the same efficiency as the direct-
current luminous or flame-carbon arc, but the alternating plain
carbon arc is much less efficient than the direct-current carbon
arc.
Arc Lamps.
68. The apparatus designed for the industrial production of
light by arc conduction, or the arc lamp, in general comprises
four elements :
(1) The current-limiting or steadying device.
(2) The starting device.
(3) The feeding device.
(4) The shunt protective device.
(1) From the volt-ampere characteristic of the arc as given
by equation (2) and curves, Fig. 46, it follows that an arc can-
not be operated directly on constant voltage supply, but in
series thereto a steadying device must be inserted; that is, a
device in which the voltage increases with the current so that
the total voltage consumed by the arc and the steadying device
increases with increase of current, and pulsations of current
thus limit themselves.
All arc lamps for use on constant voltage supply thus contain
a sufficiently high steadying resistance, or, in alternating-current
circuits, a steadying reactance.
Arc lamps for use on constant-current circuits, that is, cir-
cuits in which the current is kept constant by the source of
power supply, as the constant-current transformer or the arc
machine, require no steadying resistance or reactance.
152 RADIATION, LIGHT, AND ILLUMINATION.
Where several lamps are operated in series on constant poten-
tial mains, as two flame-carbon arcs in series in a 110-volt cir-
cuit, or five enclosed arc lamps in a 550-volt railway circuit,
either each lamp may have its own steadying resistance, or a
single steadying resistance or reactance of sufficient size may
be used for all lamps which are in series on the constant poten-
tial mains.
(2) Since the arc does not start itself, but has to be started
by forming the conducting vapor bridge between the terminals,
all arc lamps must have a starting device. This consists of a
mechanism which brings the terminals into contact with each
other and then separates them, and hereby forms the vapor
conductor, that is, starts the arc.
(3) As the arc terminals consume very rapidly in some arcs,
as the open carbon arc, and very slowly in others, as the
enclosed carbon arcs or the luminous arcs, some mechanism
must be provided which moves the terminals towards each
other at the rate at which they are consumed, and thereby main-
tains constant arc length and thus constant voltage and power
consumption.
With arcs in which the electrodes consume very slowly, as
the magnetite arc, the feeding may occur only at long intervals,
every quarter or half hour, or even less frequently, while in arcs
with rapidly consuming electrodes, as the flame arcs, practically
continuous feeding is required.
(4) The circuit between the arc electrodes may accidentally
open, as by a breakage of one electrode, or by the consumption
of the electrodes if the lamp-trimmer has forgotten to replace
them, or one of the electrodes may stick and fail to feed, and
the arc thus indefinitely lengthen. In such cases, either the
entire circuit would open, and thus all the lamps in series in
this circuit go out, or, if the circuit voltage is sufficiently high,
as in a constant-current series system, the arc lamp would be
consumed and the circuit damaged by a destructive arc. Thus
a device is necessary which closes a shunt circuit between the
lamp terminals in case the lamp voltage becomes excessive by
a failure of proper operation of the lamp.
Where only one lamp is operated, on constant potential low-
voltage supply, no such protective device is needed. If with
two or more lamps in series on constant potential supply, no
ARC LAMPS AND ARC LIGHTING. 153
objection exists, in case of the failure of one lamp, to have the
others go out also, the shunt protective device may also be
omitted, except if the circuit voltage is so high that it may
damage the inoperative lamp, as is the case with 550 volts.
When operating a number of lamps in series on constant
potential supply, as two flame lamps on 110 volts, the shunt
circuit, which is closed in case of the failure of one lamp to
operate, must have such a resistance, or reactance with alter-
nating currents, that the remaining lamp still receives its
proper voltage, even if the other lamp fails and its shunt circuit
closes. With alternating-current lamps, this does not require a
reactance of such size that the potential difference across the
reactance equals that across the lamp, which it replaces, but
the reactance must be larger; that is, give a higher potential
difference at its terminals, than the lamp which it replaces, to
leave the normal operating voltage for the remaining lamp,
since the voltage consumed by the reactance is out of phase
with the voltage consumed by the lamp.
69. For illustration, the operating mechanism of a constant
direct-current arc lamp is shown diagrammatically in Fig. 50 :
The lower electrode A is held in fixed position. The upper
electrode B slides loose in a holder C, and thus, if there is no
current through the lamp, drops down into contact with the
lower carbon, as shown in Fig. 50. When there is a current
through the arc circuit, its path is from terminal 1 through
electromagnet S, holder C, upper electrode B, lower electrode A
to terminal 2. The electromagnet S is designed so as to give a
long stroke. When energized by the current, it pulls up its
armature, the lever DD', which is pivoted at E. Through the
rod F, the lever D pulls up the clutch G. This clutch and its
operation are shown in larger scale in Fig. 51, A and B', it con-
sists of a metal piece G, which has a hole somewhat larger than
the upper electrode B. This electrode slides freely through the
hole, if the clutch G is in horizontal position, as shown in Fig. 51a.
When the rod F pulls the clutch G up, and thereby inclines the
piece G, as shown in Fig. 516, the edges p and q of the hole in
the piece G catch the electrode B, and, in the further upward
motion of D and F, raise the other electrode, B, from contact
with the lower carbon, A, and thereby start the arc. An elec-
tromagnet of many turns of fine wire, and of high resistance, P,
154 RADIATION, LIGHT, AND ILLUMINATION.
FIG. 50.
FIG. 51a.
FIG. 51b.
connected in shunt between the lamp terminals 1 and 2, acts
upon the side D' of the lever DD', opposite from the side D, on
which the series magnet S acts. With the carbons in contact
with each other, and practically no voltage between the lamp
terminals 1 and 2, the coil P receives no current, and exerts no
pull. When by the action of the series magnet S the lever D
pulls up, and the arc starts and lengthens, its voltage increases,
ARC LAMPS AND ARC LIGHTING. 155
a branch current is established through the shunt magnet P,
and this shunt magnet thus opposes the series magnet S. With
increasing arc length and thus arc voltage, a point is reached,
where the shunt magnet P counterbalances the pull of the
series magnet S, and the lever D and thereby the electrodes B
come to rest; the arc has reached its full length, that is, the
starting operation is over. As soon as, by the combustion of
the electrodes, the arc length and thereby the arc voltage be-
gins to rise, the current in the shunt magnet P, and thus its
pull, increases, while that of the series magnet S, being ener-
gized by the constant main current, remains constant; the
lever D' thus pulls up, and lowers D, and thereby, through rod
F and clutch G, the upper electrode B, and thus maintains con-
stant arc length. During the combustion of the electrodes, by
the operation of the shunt magnet P the clutch G and thereby
the upper electrode B are gradually lowered, and the arc length
thus maintained constant. Ultimately, however, the clutch G
hereby approaches the horizontal position, shown in Fig. 51 A,
so far, that the edges of the hole, p and q, cease to engage, and
the electrode B is free and drops down on the lower carbon A.
While dropping, however, the arc shortens, the arc voltage, and
thereby the current in the shunt magnet P, decreases, the pull
of this magnet decreases correspondingly, and the series magnet
S pulls the clutch G up again, thereby catches the electrode B
-usually before it has dropped quite down into contact with
the lower carbon A — and again increases the arc to its proper
length, and the same cycle of operation repeats: a gradual
feeding down of the upper electrode B by the shunt magnet
until it slips, and is pulled up again by the series magnet S.
From the same lever D is supported, by rod L, a contact-
maker K. If then the upper electrode B should stick, and thus
does not slip, when by the shunt magnet P the clutch G has been
brought into horizontal position, or, if B has been entirely con-
sumed, etc., the arc continues to lengthen and the pull of the
shunt magnet P to rise, and D thereby goes still further down
until contact-maker K closes the contacts MN, and thereby
closes a shunt circuit from terminal 1 over resistance R, con-
tacts MKN to terminal 2. In the same manner, if, by the
breaking of one electrode or any other cause, the arc should be
interrupted, for a moment the full current passes through shunt
156 RADIATION, LIGHT, AND ILLUMINATION.
magnet P, it pulls up its armature D' to its full extent, and
thereby closes the shunt circuit around the lamp.
When the current is taken off the circuit, armature D drops
down, and thereby K closes the shunt circuit, and clutch G
releases the electrode B, and it drops down into contact with
carbon A. In starting the lamp, two paths thus are available:
over series magnet S, and electrodes B and A, or over resistance
R and contacts MN. While the resistance of the former path
is very low, it is not entirely negligible. Therefore a sufficient
resistance R must be inserted in the by-path MN, so that in
starting practically all the current passes over S and the elec-
trodes, as otherwise the lamp would not start. During the
pulling up of the armature D by the series magnet S, in start-
ing, the contact K opens, before the clutch G has caught the
electrode B', that is, while the electrodes are still in contact
with each other, and the opening of contact K therefore breaks
no appreciable voltage or current, hence is sparkless.
In this lamp, no steadying resistance is used, as it is intended
for operation on a constant-current circuit. If used on con-
stant-potential circuit, as, for instance, a number in series on
550 volts, a steadying resistance R0 would be inserted, as indi-
cated at R0 in Fig. 50.
The starting of the arc is accomplished by series magnet S
and clutch G; the feeding by shunt magnet P; the protective
device is the contact MKN.
Such an arc lamp is called a differential lamp, as it is con-
trolled by the differential action of a shunt and a series
magnet.
It contains a floating system of control; that is, the upper
electrode is suspended by the balance of two forces, exerted by
the series and the shunt magnet; that is, by the current and
the voltage; the upper carbon therefore is almost continuously
moving slightly in following the pulsation of the arc resistance
which occurs during operation. Since, with the plain carbon
arc, the arc flame gives no light, this pulsation of the arc length
is not objectionable; and, since the lamp regulates very closely
and rapidly for constant terminal voltage, it is very easy on the
circuit, that is, does not tend to produce surging of current and
voltage in the circuit. The floating system of control is, there-
fore, used in all carbon arc lamps.
ARC LAMPS AND ARC LIGHTING.
157
Where a single lamp is operated on a constant-potential
circuit, the mechanism can be simplified by omitting the pro-
tective shunt circuit RMN, and omitting the shunt magnet P,
as, with a change of arc length, the main current and thereby
the pull of the series magnet S varies, and the control thus can
be done by the series magnet. Such a lamp then is called a
series lamp. An alternating-current
series lamp is shown diagrammatically
in Fig. 52.
In starting, the series magnet S pulls
up the electrode B by the clutch G,
in the same manner as in Fig. 50.
With increasing arc length and thus
increasing voltage consumed by the
arc, the current in the arc and thus
in the series magnet S decreases, and
thereby the pull of this magnet, until
it just counterbalances the weight of
the armature, and the motion stop.
With the consumption of the carbons,
the armature D, clutch G and elec-
trode B gradually move down, until
the clutch lets the carbon slip, the
arc shortens, the current rises, and
the magnet S pulls up again, the same
as in Fig. 50. A reactance x in series
with the lamp, as steadying device,
limits the current. This reactance
usually is arranged with different terminals, so that more or
less reactance can be connected into circuit, and the lamp
thereby operated, with the same arc voltage, on supply circuits
of different voltage, usually from 110 to 125 volts.
Obviously, such a series lamp can be used only as single
lamp on constant potential supply, as it regulates by the varia-
tion of current, and, with several lamps in series, the current
would vary in the same manner in all lamps. One lamp would
then take all the voltage, draw an arc of destructive length,
while the other lamps would drop their electrodes together and
go out.
70. With the luminous arc, in which the light is proportional
FIG. 52.
158
RADIATION, LIGHT, AND ILLUMINATION.
to the arc length, pulsations of the arc length, if appreciable,
give pulsations of the light, and the floating system of control,
which maintains constant voltage by varying the arc length in
correspondence with the pulsation of arc resistance, thus is
undesirable, and a mechanism maintaining fixed arc length
is required. Such a mechanism, that of the magnetite arc lamp,
is diagrammatically illustrated
in Fig. 53.
As, during operation, a
melted pool forms on the sur-
face of the electrode, the elec-
trodes are left separated from
each other when taking the
power off the circuit, since
when letting them drop to-
gether when taking off the
power — as in the carbon arc
— they may weld together and
the lamp thus fail to start
again.
A represents the lower or
negative magnetite terminal
which is movable, B, the non-
consuming upper positive elec-
trode, consisting of a piece of
copper, with heat-radiating
wings, W, which is a station-
ary and fixed part of the lamp.
C is the chimney required to
FlG- 53- carry off the smoke.
When starting, the circuit, beginning at terminal 1, passes
contacts MN, through a powerful electromagnet or solenoid 0
and resistance R, to terminal 2. The solenoid 0 pulls up its
core D, and by the clutch G raises the lower electrode A into
contact with the upper electrode, B, and thereby closes the
circuit from 1 over series coil S, electrodes B and A, to terminal
2. The series coil S pulls up the core, and thereby opens the
contact MN, thus cuts out the shunt circuit OR. The solen-
oid 0 thus loses its excitation, and drops the clutch G, and the
lower terminal A drops away from the upper terminal B by a
ARC LAMPS AND ARC LIGHTING.
159
distance which is fixed by an adjustable clutch, Q, and thus
starts an arc of definite length.
When during the consumption of this electrode A the arc
length and thereby the arc voltage rises, the shunt magnet P
increases in strength, and ultimately pulls the core F away
from the series magnet S, closes the contact MN of the shunt
circuit OR, and thereby energizes the solenoid 0. This again
raises, by the clutch G, the lower electrode A into contact with
the upper electrode B, and so repeats the cycle of operation.
If the arc between A and B opens, the solenoid S loses its
excitation, the coil F drops and closes the contact MN of the
shunt circuit OR.
If the arc resistance were perfectly constant, such a mechan-
ism would not operate satisfactorily, as the arc would have to
lengthen considerably to have the shunt coil P overpower the
series coil S sufficiently to pull the core F down, close the con-
tact MN, and thereby feed.
The resistance of an arc, and thereby, at constant length,
its voltage, pulsates, however, continuously, about as shown
diagrammatically in Fig. 54, that is, peaks of voltage of vari-
isol
110
1005
\r
FIG. 54.
ous height follow each other. Thus with an average arc volt-
age of 75, momentary peaks of 85 volts will probably be reached
every few seconds, peaks of 100 volts every few minutes, of 110
volts every half hour. Adjusting the shunt magnet P so as to
operate at 105 volts, a voltage peak above 105, which causes
the lamp to feed, would be reached about every 20 minutes.
During 20 minutes, however, the arc length does not appre-
160 RADIATION, LIGHT, AND ILLUMINATION.
ciably increase by the consumption of the electrode. Due to
the character of the arc as a pulsating resistance, such a con-
trolling mechanism thus maintains constant arc length by a
potential magnet set for a voltage considerably above the aver-
age arc voltage.
Such a mechanism, controlling for constant arc length, does
not operate for constant voltage at the lamp terminals, but
allows the pulsation of the arc resistance to appear as pulsation
of the terminal voltage. In a constant-current circuit, with
many lamps in series, these voltage pulsations of the individual
arcs overlap and have no effect on the circuit. When operating,
however, a lamp of such a mechanism on a low-voltage constant
potential circuit, a highly inductive steadying resistance is de-
sirable, to take care of the pulsations of arc voltage.
71. The open or short-burning carbon arcs of former times —
which have survived only in a few cities — were operated on
constant direct-current circuits of 9.6 and 6.6 amp. with 40 to
45 volts per lamp.
The present enclosed or long-burning carbon arcs are oper-
ated on constant-current circuits of 5 amp. and 6.6 amp.
direct current, or of 6.5 and 7.5 amp. alternating current, with
about 72 volts at the lamp terminals. They are operated as
single lamps, of 5 to 9 amp. on direct- or alternating-current
constant potential circuits of 110 to 125 volts, or two lamps in
series on circuits of 220 to 250 volts.
The flame-carbon arcs, as short-burning open arcs, are usually
operated two in series on constant-potential circuits of 110 to
125 volts, or four in series on circuits of 220 to 250 volts, with
10 to 15 amp. in the arc.
The luminous arcs are operated on 4- and 6.6-amp. constant
direct-current circuits (magnetite lamp), with 75 volts per
lamp, and on 3- and 4.5-amp. constant alternating-current cir-
cuits (titanium-carbide arc), with 80 volts per lamp.
Arc Circuits.
72. Arc lamps are built for, and operated on, constant-poten-
tial supply, and on constant-current supply. In general, the
constant-potential arc lamp is less efficient, as voltage and
thereby power is consumed in the steadying resistance which is
required to limit the current, that is, to give an approximate
ARC LAMPS AND ARC LIGHTING. 161
constant-current effect, as discussed above. In alternating-
current circuits, reactance may, and usually is, employed in-
stead of the steadying resistance, and the waste of power thereby
greatly decreased. Voltage, however, is still consumed and the
power factor lowered.
An additional waste of energy generally occurs in constant-
potential arc-lamp circuits, due to the standard distribution
voltages of low-potential circuits being higher than necessary
for the operation of a single lamp, but too low for the operation
of two lamps in series. Thus with an enclosed 5-amp. carbon
arc lamp, with about 70 volts at the arc, a supply voltage of
95 to 100 volts would be sufficiently high above the stability
curve of the arc (Fig. 46) to give steady operation. Distri-
bution voltages, however, vary between 110 to 130 volts, and
the difference thus must be consumed in resistance, giving an
additional waste. (Except in those rare cases, where as steady-
ing resistance some useful devices, as incandescent lamps, can
be employed.) With an enclosed arc lamp on a 125- volt cir-
cuit, only 36 volts, or 29 per cent, are usefully employed in
heating the carbon terminals and thereby producing the light,
while the remaining 71 per cent is wasted in the resistance
and in the non-luminous arc flame. Somewhat better are the
conditions when operating two high-current open arcs, as two
flame lamps, in series on such a circuit. However, at the lower
distribution voltage, as 110 volts, the supply voltage may be
already so close to the stability limit of the arc that the arcs
are not as steady as desirable.
The low-current, long luminous arcs of electro-conduction, as
the magnetite arc, can in general be operated only with diffi-
culty on circuits of 110 to 125 volts, and therefore are, for
constant-potential service, frequently designed for operation as
single lamps on 220 to 250 volts supply, with extra great arc
length.
For indoor illumination, constant-potential arc lamps must
obviously be used, as safety does not permit the introduction
of the high-voltage series arc circuits into houses. For out-
door illumination, as street lighting, in the United States the
constant-current arc lamp is, with the exception of the interior
of a few very large cities, as New York, used exclusively, due to
its greater efficiency, and the greater distance to which the cur-
162 RADIATION, LIGHT, AND ILLUMINATION.
rent can be sent at the high voltage of the constant-current
circuit. In American towns and cities, where arc lamps are
used for street lighting, practically always the entire city up to
the farthest suburbs is lighted by arc lamps, and frequently arc
lamps installed even beyond the reach of the high-potential
primary alternating-current supply. To reach such distances
with low-voltage constant-potential supply, is impossible, and
thus the constant-current series system becomes necessary. In
European cities, where a prejudice exists against high-voltage
constant-current circuits, and people are satisfied to have arc
lamps only in the interior of the city, and leave the lighting of
the suburbs to gas lamps, constant-potential street lighting is
generally employed, and is eminently satisfactory within the
limitations with which European cities are satisfied, but would
be impossible in the average American city.
Where plain carbon arcs are used in American cities the
enclosed arc lamp is exclusively installed, and open arc lamps
have survived only in a few exceptional cases, mainly where
political reasons have not yet permitted their replacement by
modern lamps. The lesser attention required by the enclosed
arc lamp — weekly trimming instead of daily with the open arc
lamp — has been found to make it more economical than the
open arc lamp of old. In Europe, where labor is cheaper, and
the daily attention not considered objectionable, the open or
short-burning arc lamp has maintained its hold, and the en-
closed arc lamp has never been used to any great extent. With
the development of the flame carbon, the flame arc, therefore,
has found a rapid introduction in Europe, while in the United
States it has been excluded from use in street lighting, due to
its short-burning feature, which requires daily trimming, and is
used only for decorative purposes, for advertising, etc., and for
low-grade interior lighting, as foundries, etc.
In spite of the lower efficiency of the alternating carbon arc,
the constant-current circuits used for arc lighting are generally
alternating, due to the greater convenience of generation of
alternating current, and constant direct-current arc circuits
used only where the city or the electric light company lays stress
on the efficiency of light production.
While the development of the constant-current mercury arc
rectifier has made the generation of constant direct current
ARC LAMPS AND ARC LIGHTING. 163
almost as simple and convenient as that of alternating current,
this has very little increased the use of the direct-current en-
closed arc lamp, but when changing to direct current sup-
ply, usually the arc lamp is also changed to the luminous arc,
the magnetite lamp, which gives more light and consumes less
power.
In constant-current arc circuits, usually from 50 to 100
lamps are operated in series on one circuit, with circuit volt-
ages of 4000 to 8000 volts. Seventy-five-lamp circuits, of 6000
volts, probably are the most common.
73. Constant direct current was produced by so-called "arc
machines" or "constant-current generators." Of these only
the Brush machine has survived, and is now also beginning to
disappear before the mercury arc rectifier, which changes the
alternating current of the constant-current transformer to direct
current without requiring moving machinery.
The Brush machine in its principle essentially is a quarter-
phase constant-current alternator with rectifying commutator.
An alternator of low armature reaction and strong magnetic
field regulates for constant potential: the change of armature
reaction, resulting from a change of load, has little effect on
the field and thereby on the terminal voltage, if the armature
reaction is low. An alternator of very high armature reaction
and weak field, however, regulates for constant current: if the
m.m.f., that is, the ampere-turns required in the field coil to
produce the magnetic flux, are small compared with the field
ampere-turns required to take care of the armature reaction,
and the resultant or magnetism-producing field ampere-turns
thus the small difference between total field excitation and
armature reaction, a moderate increase of armature current
and thereby of armature reaction makes it equal to the field
excitation, and leaves no ampere-turns for producing the mag-
netism; that is, the magnetic flux and thereby the machine
voltage disappear. Thus, in such a machine, the current out-
put at constant field excitation rises very little, from full volt-
age down to short circuit, or, in other words, the machine
regulates for approximately constant current. Perfect constant-
current regulation is produced by a resistance shunted across the
field, which is varied by an electromagnet in the machine circuit,
and lowered — that is, more current shunted through it, and
164 RADIATION, LIGHT, AND ILLUMINATION.
thereby the field excitation decreased — if the machine cur-
rent tends to rise by a decrease of the required circuit voltage,
and inversely.
The constant-current regulation of the arc machine thus is
not produced by its so-called " regulator/' but approximate
constant-current regulation is inherent in the machine design,
and the regulator merely makes the regulation perfect.
A more explicit discussion of the phenomena in the arc
machine, and especially its rectification, is given in Chapter III
of Section II of "Theory and Calculation of Transient Electric
Phenomena and Oscillations."
In alternating-current circuits, approximate constant-current
regulation is produced by a large reactance, that is, by self-
induction, in the circuit. In transformers, the self-induction is
the stray field, or the leakage flux between primary coil and
secondary coil. In the constant-current transformer, which is
most generally used for constant alternating-current supply
from constant alternating voltage, the primary turns and the
secondary turns are massed together so as to give a high mag-
netic stray flux between the coils. Such a transformer of high
internal self-induction, or high stray flux, regulates approxi-
mately for constant current. Perfect constant-current regula-
tion is produced by arranging the secondary and the primary
coils movable with regard to each other, so that, when low cir-
cuit voltage is required, the coils move apart, and the stray
flux, that is, the reactance, increases, and inversely. The
motion of the coils is made automatic by balancing the magnetic
repulsion between the coils by a counter- weight. A discussion
of the constant-current transformer and its mode of operation
is given in "Theory and Calculation of Alternating Current
Phenomena," Fourth Edition, page 85.
In the so-called "constant-current reactance," the two coils
of the constant-current transformer are wound for the same
current, and connected in opposition with each other, and in
series to the arc circuit into the constant-potential mains.
With the coils close to each other, the reactance is a minimum,
and it is a maximum with the coils their maximum distance
apart.
The constant-current reactance has the advantage of greater
cheapness, but also has the serious disadvantage that it connects
ARC LAMPS AND ARC LIGHTING. 165
all the arc circuits electrically with the constant-potential alter-
nating-current system, and any ground in an arc circuit is a
ground on the constant-potential supply system. As grounds
are more liable to occur in arc circuits, the constant-current
reactance is therefore very little used, and generally the con-
stant-current transformer preferred, as safer.
In the constant direct-current mercury-arc rectifier system,
the constant-potential alternating-current supply is changed to
constant alternating current by a constant-current transformer,
and the constant alternating current then changed to constant
direct current by the mercury-arc rectifier. An explicit dis-
cussion of the phenomena of the constant-current mercury arc
rectifier is given in Chapter IV of Section II of " Theory and
Calculation of Transient Electric Phenomena and Oscillations."
If the constant-current arc circuit accidentally opens, with a
Brush machine as source of supply, the voltage practically
vanishes, as the machine has series field excitation, and thus
loses its field on open circuit. The constant-current trans-
former, however, maintains its voltage, and gives maximum
voltage on open circuit. The mercury arc rectifier, when sep-
arately excited by a small exciting transformer, also maintains
its voltage on open circuit. If, however, after starting, the
excitation is taken off, that is, the exciting circuit opened, as
is permissible in a steady arc circuit, the voltage in the arc
circuit disappears if the arc circuit is opened. Inversely, when
connecting an arc circuit to a Brush arc machine, an appre-
ciable time elapses while the voltage of the machine builds
up, while with the constant-current transformer and thus also
with the constant-current mercury arc rectifier system, full volt-
age exists even before the circuit is closed.
LECTURE IX.
MEASUREMENT OF LIGHT AND RADIATION.
74. Since radiation is energy, it can be measured as such
by converting the energy of radiation into some other form of
energy, as, for instance, into heat, and measuring the latter.
Thus a beam of radiation may be measured by having it
impinge on one contact of a thermo-couple, of which the other
contact is maintained at constant temperature. A galvanom-
eter in the circuit of this thermo-couple thus measures the
voltage produced by the difference of temperature of the two
contacts of the thermo-couple, and in this manner the temper-
ature rise produced by the energy of the incident beam of radia-
tion is observed.
Probably the most sensitive method of measuring even very
small amounts of radiation is the bolometer. The beam of
the radiation (or after dissolving the beam into a spectrum,
the wave length of which the power is to be measured) impinges
upon a narrow and thin strip of metal, as platinum, and thereby
raises its temperature by conversion of the radiation energy
into heat. A rise of temperature, however, produces a rise of
electric resistance, and the latter is measured by enclosing the
platinum strip in a sensitive Wheatstone bridge. The rise of
temperature of the platinum strip by the small power of radia-
tion obviously is so small that it could not be observed by
any thermometer. Electric resistance measurements, however,
can be made with extreme accuracy, and especially extremely
small changes of resistance can be measured. Thus a change
of resistance of 1 in a million and, with very sensitive measure-
ments, even many times smaller changes can be observed. As
1 deg. cent, produces a resistance change of about 0.4 per cent,
a change of one millionth corresponds to a temperature rise
°f ?tfW deg. cent. Thus, by the bolometer, extremely small
amounts of radiation can be measured, as, for instance, the
power of the moon's radiation, etc.
166
MEASUREMENT OF LIGHT AND RADIATION. 167
The total radiation energy of a body for a given time can be
measured by absorbing it and measuring the heat produced by
it, as; for instance, the amount of ice melted in a calorimeter.
Any particular range of the total radiation, as, for instance, the
total visible radiation, can be measured in the same manner
by passing the radiation first through a body which absorbs
that part which is not desired, for instance, a body transparent
to visible, but opaque to invisible radiation. As no body is
perfectly transparent to one, perfectly opaque to another radi-
ation, the separation of the radiation by absorption is nec-
essarily incomplete, and correction must therefore be made
in the result. This makes this method rather inconvenient
and inaccurate. Even when measuring the total radiation by
absorption in a calorimeter, it is practically impossible to
collect the total radiation without either losing some, or
including energy, which is not radiation, but heat conduc-
tion or convection. Obviously, by enclosing the radiator in
the calorimeter, the latter would measure not only the radi-
ation, but also the power lost by heat conduction, convec-
tion, etc.
Sometimes the power of radiation can be measured by meas-
uring input and losses. Thus, in an incandescent lamp, the
electric-power input is measured, and the power lost by heat
conduction and convection estimated if not entirely negligible.
In those cases in which all or most of the energy supplied is
converted into radiation, as in an incandescent lamp, this
method is the most exact. However, it can directly measure
only the total radiation power. To measure the different parts
of the radiation so as to determine separately the power in the
visible, the ultra-red, and the ultra-violet range, the method of
input and losses can be used to give the total radiation power,
and, by bolometer or other means, the relative powers of the
component radiations measured in a beam of light. From the
total radiation and the ratio of its components, then, follows
the values of radiation power of the components.
75. Light, however, cannot be measured by any of the pre-
ceding methods, since light, in the sense in which it is con-
sidered photometrically, is not power, but is the physiological
effect of certain wave lengths of radiation, and therefore can-
not be measured, physically, as power, but only physiologically,
168 RADIATION, LIGHT, AND ILLUMINATION.
by comparison with other physiological effects of the same
nature.
The power of visible radiation obviously can be measured,
and thus we can express the power of the visible radiation of
a mercury lamp or an incandescent lamp in watts. But the
power of visible radiation is not proportional to the physiologi-
cal effect, and thus not a measure thereof. One watt of green
radiation gives many times as great a physiological effect, that
is, more light, as does one watt of red or violet radiation, and,
besides, gives a different kind of physiological effect: a differ-
ent color.
The unit in which illuminating value of light, or its intensity,
is expressed as the "candle-power," is, therefore, a physiological
and not a physical quantity, and hence it has no direct or con-
stant relation to the unit .of power, or the watt. The unit of
light intensity has been chosen by convention: as the physio-
logical effect exerted on the human eye by 5 sq. mm. of melting
platinum, or by a flame burning a definite chemical compound
— as amyl acetate or pentane — at a definite rate and under
definite conditions, etc.
Broadly, therefore, the conception of a chemical equivalent of
light, that is, a relation between candle power and watt, is
irrational, just as, broadly, a relation between time and distance
is irrational; that is, just as distance cannot be expressed by
the unit of time, so candle power cannot be expressed by a
unit of power, as the watt. A relation between two such
inherently different quantities can be established only by an
additional conventional assumption, and varies with a change
of this extraneous assumption. Thus stellar distances are
measured in " light years," that is, by the distance traveled by
the light in one year, as unit. So also the physiological effect
of one definite color of light, as that of the green mercury line,
or the yellow sodium line, or the red lithium line, can be related
to the unit of power, or the watt, and we may speak of a me-
chanical equivalent of green light, or of yellow light, or of red
light. When doing so, however, we give to the term " mechan-
ical equivalent" a different meaning from what it has in physics,
for instance, as "mechanical equivalent of heat." The latter
is the constant relation between two different forms of the
same physical quantity, while, for instance, the "mechanical
MEASUREMENT OF LIGHT AND RADIATION. 169
equivalent of green light " is the relation between a physiolog-
ical effect and the physical quantity required to produce the
effect, and thus is not necessarily constant, but may, and does,
vary with the intensity of the effect, the individuality of the
observer, etc. It appears, however, that at higher intensities
the relation is very nearly constant and the same with differ-
ent observers, so that it is possible to express the physiological
effect of a definite wave length of radiation, within the accuracy
of physiological measurements, by the power consumed in pro-
ducing this wave length of radiation; but it becomes entirely
impossible to compare physiological effects of widely different
wave lengths by comparing the power required to produce them.
When speaking of mechanical equivalent of light, it thus
must be understood in the extended meaning of the word, as
discussed above.
76. In photometry, and in general in illuminating engineer-
ing, it is of essential importance to keep in mind this difference
in the character of light, as physiological effect, and radiation,
as physical quantity of power. This is the reason why all
attempts to reduce photometry to a strictly physical measure-
ment, and thereby bring photometric determinations up to
the high grade of exactness feasible in physical observations,
have failed and must necessarily fail; we cannot physically
compare an effect as light, which is not a physical quantity,
but somewhere in all photometric methods the physiological
feature, that is, the judgment of the human eye, must always
enter.
Photometric tests therefore can never have the accuracy of
strictly physical determinations. All attempts to eliminate
the judgment of the human eye from photometry, by replac-
ing it by the selenium cell, or the photographic plate, or
Crookes' radiometer, etc., necessarily are wrong in principle and
in results: some of those instruments, as the bolometer, the
radiometer, etc., compare the power of the radiation, others,
as the selenium cell or the photographic plate, the power of
certain changes of radiation, but their results are comparisons
of power, and not of physiological effects, and thus they can-
not be of value in measurement of illuminating power.
Measurements of light thus are made by comparison with
an arbitrarily chosen conventional unit, a primary standard
170 RADIATION, LIGHT, AND ILLUMINATION.
of light, as " standard candle," or a duplicate or multiplicate
thereof. Obviously, in measurements of light, usually not the
primary standard of light is used, but a more conveniently
arranged secondary standard of light, that is, a standard which
has been calibrated by comparison, directly or indirectly, with a
primary standard.
77. The most accurate method of comparing lights is the
zero method, as represented by the different types of photom-
eters. The illumination produced by the two different sources
of light — the one to be tested and the standard — are made
equal by changing the relative distances of the sources. At equal
illumination their intensities are proportional to the square of
their distances. Thus, for instance, in the bunsen photometer,
as shown diagrammatically in its simplest form in Fig. 55, the
FIG. 55.
two white screens A and B are illuminated, the one, A, by the
light, L, which is to be tested, the other, B, by the standard S,
as a calibrated or standardized 16-cp. incandescent lamp, and
then either L or S or both are moved until, seen from (7, the
two sides A and B of the screen become equal, that is, the divid-
ing line C between them disappears. When this is the case,
L -T- S = x2 -T- 7/2, where x and y are the two distances of the
sources from the screen.
Different modifications of the bunsen photometer are most
commonly used.
As the sensitivity of the eye to differences of illumination is
not very great, usually a number of readings are taken on the
photometer, and then averaged.
For testing incandescent lamps, L, as standard S, a calibrated
incandescent lamp is used, operated on the same voltage supply,
so that fluctuations of light caused by minor fluctuations of sup-
ply voltage eliminate by appearing in both sources L and S.
MEASUREMENT OF LIGHT AND RADIATION. 171
For similar reasons, when testing gas lamps or other flames,
L, as S, a flame standard, as the pentane lamp, is used, so that
the effect of barometric pressure, humidity of the air, etc.,
appears in both lamps and thereby does not appreciably affect
the comparison of their light.
A quick and approximate method of comparison of sources
of light is given by the shadow photometer by moving an
object between the two lamps until the two shadows of the
object give the same darkness. When this is the case, the
illumination at the object is the same, and the intensities of
the two sources are then proportional to the square of their dis-
tances from the object. Street lamps can, in this manner, be
rapidly compared, with fair
accuracy, by pacing the
distance from the one to
the other, and noting when
the two shadows of the
observer are equal in dark-
ness. If then at x steps
from the one lamp, Llt the
shadows are equal, and y
further steps are required
to reach the second lamp,
L0, it is :
0
A very convenient form
of photometer, which gives
good results even where
the two lights are of some-
what different color, is the FlG 56
paraffine photometer. A
block of paraffine is cast, as shown in Fig. 56, divided by a
sheet of tinfoil in the center C, and covered with tinfoil except
at the top and on the sides A and B. It is advantageous to
have the center sheet of tinfoil C perforated by a hole D.
The block of paraffine then is held so that the side A is illu-
minated by the one lamp, L, the side B by the other lamp, S, as
shown in Fig. 57. As paraffine is translucent, the entire block
then appears luminous, and a beam of light is seen traversing
172 RADIATION, LIGHT, AND ILLUMINATION.
the block from the hole D, on the side which receives less light.
By moving the paraffine block between the lamps L and S,
until both sides of it are of the same luminosity, that is, the
dividing line C and the beam cast by hole D disappear, equality
of the two illuminations can be located rapidly and with great
accuracy.
FIG. 57.
78. When comparing lamps giving light of the same color, as
incandescent lamps of the same filament temperature, that is,
the same efficiency, exact comparisons can be made — within
the limits of sensitivity of the eye for intensity differences —
by the photometer by making the two sides A and B of the
Bunsen photometer screen, or the two halves of the paraffine
block, identical, that is, making the dividing line C disappear.
If, however, the color of the two lights is not the same, as, for
instance, when comparing a tungsten lamp and an ordinary
incandescent lamp, no position of the photometer can be found
where the dividing line C between A and B (Figs. 55, 57) dis-
appears, but a color difference always remains. To make a
comparison, it is therefore necessary for the eye to judge
when the two sides A and B are of the same intensity while of
different colors. If the color difference is small, as between two
different types of incandescent lamps, this can be done with
fair accuracy, though obviously not as accurately as the com-
parison of lights of identical colors. If, however, the color
difference is great, as between the mercury arc and the orange-
yellow carbon filament lamp, the uncertainty of equality of
the intensity of illumination becomes very great, and constant
errors appear, due to the difference of the physiological effect
of different colors, and differences also appear between differ-
ent observers, so that the photometric comparison of light
sources of greatly different colors is quite unreliable, and that
not merely by inaccuracy, but by unknown and individual con-
stant errors.
In such cases, frequently lights of intermediary color are
used to reduce the differences in each observation. Thus the
carbon filament lamp is compared with the tungsten lamp, the
MEASUREMENT OF LIGHT AND RADIATION. 173
tungsten lamp with the carbon arc lamp, and the latter with
the mercury arc lamp. Hereby the uncertainty of each obser-
vation is reduced by the reduced color difference. In the final
result, however, the comparison of the carbon incandescent-
lamp standard and the mercury arc lamp no advantage is
gained, because the errors of the successive measurements add.
Especially is this the case with the constant errors, that is,
errors due to the specific color effect, and in consequence thereof
the inaccuracy of the final result is not much better than it
would be by single and direct comparison.
A photometer which is sometimes used for comparing lights
of different color, and is based on a different principle from
either of the above discussed instruments, is the flicker pho-
tometer. In its simplest form it consists of a stationary disk,
illuminated by the one lamp, and a rotating half disk or sector
in front of it, which is illuminated by the other lamp. At slow
rotation a flicker shows, which disappears if the speed be-
comes sufficiently high. It is obvious that the more nearly
equal the effect on the eye of the two illuminations — that of the
stationary disk and that of the revolving sector — the lower is
the speed at which the flicker disappears, and, by adjusting the
distances of the two lamps so as to cause the flicker to dis-
appear at the minimum speed, the instrument indicates equality
of the effect of the two successive illuminations on the eye.
This is frequently considered as representing equality of the
illumination, and the instrument in this manner used to com-
pare illuminations. There is, however, no reason why this
should be the case, but, on the contrary, it is improbable. As
the persistence of vision, and in general the physiological effects
of different colors, are different, the flicker photometer must be
expected to have a constant error which increases with color
difference; that is, it does not compare lights of different color
by their illuminating values, but by some other feature not
directly related thereto.
79. The photometer thus cannot satisfactorily compare lights
of different colors. After all, this is obvious: the photom-
eter compares by identity, but lights of different colors can-
not be identical, and thus two such lights cannot be more
broadly compared than any other two quantities of different
character; that is, a green light can no more be equal to a red
174 RADIATION, LIGHT, AND ILLUMINATION.
light than a piece of stone can be equal to a piece of ice. A
comparison of quantities of different nature is possible only
regarding particular features of the quantities which they have
in common. Thus a piece of stone and a piece of ice can be
compared regarding their weight, or their density, etc. In the
same manner, two different colors of light, or in general two
different frequencies of radiation, can be compared by any
feature which they have in common. Thus, for instance, the
photographic plate compares them in their chemical activity,
the bolometer by their physical energy.
Light is used for seeing things by, that is, distinguishing
objects and differences between objects. Regarding this feature,
the distinction of objects given by them, different colored lights
can be compared, and a green light can be made equal to a red
light in illuminating value.
It thus means that any two lights, regardless of their color,
have the same intensity if, at the same distance from them,
objects can be seen with the same distinctiveness, as, for in-
stance, print read with equal ease. The only method, therefore,
which permits comparing and measuring lights of widely differ-
ent color is the method of " reading distances," as used in the
so-called luminometer. It after all is the theoretically correct
method of comparison, as it compares the lights by that prop-
erty for which they are used. Curiously enough, the lumi-
nometer, although it has the reputation of being crude and
unscientific, thus is the only correct light-measuring instrument,
and the photometer correct only in so far as it agrees with the
luminometer, but, where luminometer and photometer disagree,
the photometer is wrong, as it gives a comparison which is
different from the one shown by the lights in actual use for
illumination.
The relation between luminometer and photometer for meas-
uring light intensity, therefore, is in a way similar to the relation
between spark gap and voltmeter when testing the disruptive
strength of electrical apparatus: while the voltmeter is fre-
quently used, the exact measure of the disruptive strength is
the spark gap and not the voltmeter, and, where the spark gap
and voltmeter disagree, the voltmeter must be corrected by the
spark gap. In the same manner the luminometer measures
the quality desired — the illuminating value of the light — but
MEASUREMENT OF LIGHT AND RADIATION. 175
FIG. 58.
the photometer may be used as far as it agrees with the lumi-
nometer.
80. The luminometer can hardly be called an instrument,
but it is merely a black box, as shown in Fig. 58, to screen off
all extraneous light, and
allow only the light of the
source which is to be ob-
served, to fall on the print.
The print obviously must
be black on white, that is,
complete absorption and
complete reflection, so as
not to discriminate in
favor of particular colors.
No great accuracy could
be reached by merely com-
paring the ease of reading
the same kind of print with different sources of light. A high
accuracy, however, is reached by using a print which does not
give definite words — in which letters which are not clearly
seen cannot be guessed from the sense of the word or sentence
— but a jumble of letters, capitals and small letters, arranged in
meaningless words.
Such a luminometer chart is given below:
Amhof dirito amritu, Lisno ladse pemrane odo Ulay
Foresca 1598720 woleb noitaidar. Ybod ergy may
Pewos ex Idetnera, bsor poge Morf Tenscerophop War-
dog; Omsk whykow efforau tespo ygnew col Brispo
Monas albo darmosphor? Cottef vol Demno myo
36802 Erbtomy, quot Hiaworu pio Nio cuguab Qaphla-
qua H 530 K b n q; 267 Lloysir baraka nunc, cinq
Viamara W x 4 zoliaq kama nambosi erianoscum.
Zaraz didym fore ik yiquia Fumne.
With such a printed chart in the luminometer, the observer
moves towards the light or away from it — or the light is
moved, with the observer stationary — until a point is found
at which the large letters, as the capitals, can be clearly dis-
tinguished, but the small letters are indistinguishable. This
point can be found with great sharpness, and the accuracy of
176 RADIATION, LIGHT, AND ILLUMINATION.
observation by the luminometer when used in this manner is
nearly as great as that of the ordinary photometer, but, unlike
the photometer, the luminometer gives consistent and reliable
readings even with widely different colors of light.
The comparisons made by the luminometer of widely differ-
ent colored lights by different observers agree remarkably
well, showing that the distribution of color sensitivity is prac-
tically the same in different human eyes. Only occasionally a
person is found with abnormally low sensitivity for some par-
ticular color — this obviously is not a fault of the instrument,
but in the nature of the measured object, which is a physiologi-
cal effect, and as such may be different in different persons.
The luminometer can be still further improved by illuminat-
ing one half of the printed chart from the one, the other half
from the other, source of light, and then moving the two sources
to such distances that the small letters on both sides of the chart
become indistinguishable, while the capitals are distinguishable.
As well known, the luminometer is largely used for measuring
street illumination, as it is very simple and requires no special
technical training. Such observations, where the distances are
measured by pacing, are crude, and, to get exact results by the
luminometer, the same care is required as when using the pho-
tometer.
The limitation of the luminometer, as generally used, is that
it compares lights at constant and relatively low intensity of
illumination. The relative intensity of light sources of differ-
ent colors changes however over a wide range with the inten-
sity of illumination at which they are compared, as discussed
in Lecture III. A complete comparison of different colored
lights therefore requires measurements at different intensities
of illumination.
With a photometer, the intensity of illumination can usually
be varied over a wide range by bringing the light sources
nearer to the screen or removing them farther. In the lumi-
nometer, only a moderate change of the intensity of illumina-
tion, at which the comparison is made, can be produced by
using different sizes of print, and the interpretation of such
tests is difficult.
A wide and definite range of intensities of illumination, at
which comparison of the light sources is made by the lumi-
MEASUREMENT OF LIGHT AND RADIATION. 177
nometer, can be secured by using gray print on white back-
ground, and lights of different colors thereby compared over
a wide range of illuminations.
With a luminometer chart of gray letters, of albedo a, on
white background, the illumination or light flux density, at
which the luminometer readings are made as described above,
is:
where i0 is the illumination or light flux density when using
black print on white background.
81. Since light is a physiological effect, the measurement of
this effect requires a physiological unit, which is more or less arbi-
trarily chosen. Such a unit may be a unit of light, that is, of
light intensity or light flux, as a flame, or it may be a unit of
light-flux density or illumination, that is, of light flux per unit
area.
Thus, a fairly rational unit of light-flux density or illumination
would be the illumination required at the limits of distinguish-
ability of black print of a specified type, on white back-
ground, that is, the light flux per unit area by which, with such
black print on white background, the capitals and large letters
can still be distinguished, while the small letters are indistin-
guishable.
Usually so-called " primary standards " have been chosen as
units of light intensity. Violle recommended as standard the
light at right angles from 1 sq. cm. of melting platinum. (Ap-
proximately 20 cp.) This unit has never been introduced,
partly due to the difficulty of producing it, partly due to the
unsuitability of platinum for this purpose: platinum gives
gray-body radiation, therefore any impurity, as a trace of car-
bonized dust, may increase the light.
Candles have been largely used for standards, as the name of
the unit implies, made and burned under definite specifications.
As individual candles vary widely in their light, the use of the
candle as standard necessarily is very crude and inaccurate,
and thus unsatisfactory.
The only primary standard which has found extensive and
international use is the amyl-acetate lamp of Hefner. This is
a lamp burning arnyl acetate at a definite rate, with a definite
178 RADIATION, LIGHT, AND ILLUMINATION.
height of flame and definite conditions regarding air pressure
and humidity. This Hefner lamp, or German candle, equals
about 90 per cent of the British candle and equals 90 per cent of
the international candle. Amyl acetate has been chosen, as it
can easily be produced in chemical purity, and gives a good
luminous flame. The flame, however, is somewhat reddish, thus
markedly different from the color of the carbon incandescent
lamp, and departs still much more from that of the tungsten
lamp. Instead of amyl acetate, pentane has been used and is
still used. It gives a somewhat whiter flame, but the pentane
lamp is not as constant.
However, the Hefner lamp, while universally used as pri-
mary standard, is altogether too inconvenient for general pho-
tometric use, and, for this purpose, usually incandescent lamps
are employed which have been compared with, and standard-
ized by, the Hefner lamp. In reality, from these standard
incandescent lamps, by comparison, other incandescent lamps
have been standardized, and so on, until of late years the
Hefner lamp has been finally abandoned as primary standard of
light, and we have no primary standard; but the standard of
light is maintained by comparison with incandescent lamps
kept for this purpose; that is, it is maintained by duplication of
samples, and by international agreement an incandescent lamp
unit has been adopted as the standard or " international candle."
82. A number of primary standards have lately been pro-
posed, but none has yet been much developed.
Some work was done on the acetylene flame, burning in
oxygen. It has a very suitable white color, but its intensity is
very sensitive to slight impurities of the acetylene, and such
impurities, as hydrogen, are difficult to avoid.
A suitable unit appears to be the normal temperature radiation
at specified temperature, and the temperature could be defined
by the ratio of the radiation power of definite wave lengths.
Thus, such a unit would be an incandescent lamp, radiating x
watts at such temperature that the power radiated between wave
lengths 45 and 55 bears to the power radiated between wave
lengths 60 to 70 the ratio y. The radiated power x could prob-
ably be determined from electric power input and losses. Such
a unit would probably be replaceable with considerable exact-
ness, but would still be arbitrary.
MEASUREMENT OF LIGHT AND RADIATION. 179
A further possible unit would be the light given by one watt
visible radiation, by normal temperature radiation at a definite
temperature — the latter specified and measured by the ratio
of radiation power of two different ranges of wave length.
Such definition would base the physiological effect, under speci-
fied conditions of temperature, on the unit of power, or the
watt, as unit of light. Its disadvantage is the difficulty of
measuring the power of the total visible radiation, since at the
ends of the visible spectrum the power is high and the physio-
logical effect low, and a small error in the limits of the spectrum
would make a considerable error in the result.
More satisfactory, therefore, appears the derivation of a
primary standard of light by combining three primary colors of
light in definite power proportions. Thus, choosing three lines
of the mercury spectrum — in the mercury arc in a vacuum,
perfect steadiness and high intensity can easily be produced —
in the red, green and blue, about equidistant from each other,
these three radiations would be combined in definite propor-
tions — chosen so as to give the desired color of the light,
probably a yellowish white — and in such qualities as to
give one watt total radiation, or, if as unit the illumination
is used, to give one microwatt per sq. cm.; that is, the
standard of illumination would be the illumination produced
by one microwatt of radiation power, composed of the three
wave lengths of the three chosen mercury lines, in definite
proportions.
Such a standard, derived by combination of definite wave
lengths, which are easily reproducible, appears the most satis-
factory in regard to permanence. It would incidentally give a
numerical expression to color values, as any color then would
be represented by the numerical ratio of the power of the three
standard spectrum radiations, which, mixed together, give the
color.*
83. Light is produced for the purpose of illumination. The
raw material used in illumination is the flux of light issuing
from the illuminant. The important characteristic of the illu-
minant, by which it is judged, thus is the total flux of light
issuing from it, and its measurement one of the main objects
of photometry.
* Proc. A. I. E. E., (1908).
180
RADIATION, LIGHT, AND ILLUMINATION.
The photometer or luminometer, however, gives the light
intensity in one direction only. Thus, to measure the total
flux of light, the light intensity in all directions in space
must be determined, and added, or averaged, to get the
average intensity of light, usually called the "mean spherical
intensity."
If the light intensity were the same in all directions, one
single photometric observation would give it, and therefrom, by
multiplying with 4 TT, the total flux of light would be obtained.
This, probably, is never the case.
Many illuminants, however, give a symmetrical distribution
of light around an axis, so that the distribution curve is the
same in all meridians. This is practically the case with the or-
dinary incandescent lamp with oval filament, and also with the
tantalum and the tungsten lamp. Thus if the curve, shown in
Fig. 59, is the distribution curve in one meridian, it is the same
FIG. 59.
in every other meridian, and for photometric test of the illumi-
nant it is sufficient to measure the light intensities in one merid-
ian only, for instance, from 10 to 10 degrees. To get herefrom
the mean or average intensity, it would obviously be wrong to
merely average all the intensities under equal angles, since the
equatorial intensity covers a far greater area — a zone of 10 de-
grees width and 2 x circumference — than the intensity of lati-
tude <j>j that is, under angle <f> from the horizontal: the latter
covers a zone of 10 degrees width and 2 it cos $ circumference,
and the polar intensity covers only a point.
To get the total flux of light, the intensity under each angle <£
MEASUREMENT OF LIGHT AND RADIATION. 181
thus is to be multiplied with the area of the zone which it
covers, 2 nd cos <j>, where d is the angular width of the zone
(10 deg., for instance), and then added. The average or mean
spherical intensity then is derived herefrom by dividing with
the surface of the sphere, or by 4 re.
Thus, to get the mean spherical intensity from the distribu-
tion curve, the instantaneous values of intensity, taken under
equal angles d, are multiplied each by cos <£, then added, and
ft
the sum multiplied by -, where d, the angular distance under
2
which observations are taken, is given in radians, that is,
10 deg. gives d = — - TT. This usually is done graphically.
180
Occasionally, as in incandescent lamps with single-loop fila-
ment, the light intensity is not the same in all meridians, but a
maximum in two opposite meridians: at right angles to the
lamp, and a minimum in the two meridians at right angles to
the former, giving a horizontal or equatorial distribution of
FIG. 60.
light intensity about as shown in Fig. 60. In this case the
horizontal distribution curve may also be determined photo-
metrically, averaged so as to give the mean horizontal intensity
182 RADIATION, LIGHT, AND ILLUMINATION.
and the ratio of the mean horizontal intensity to the maximum
horizontal intensity (or any other definite horizontal inten-
sity); and the mean spherical intensity, as derived from the
meridian of maximum horizontal intensity (or any other definite
horizontal intensity), is multiplied with this ratio to get the
real mean spherical intensity. Usually in this case measure-
ments are taken only in one meridian, but during the test the
lamp rotated around its vertical axis with sufficient speed, so
that each observation in the meridian, under angle <£, in reality
is the mean intensity in the direction <f>. Thus, in incandes-
cent lamp tests, usually the lamp is revolved, so as to average
between the different meridians.
As the distribution of intensity in the meridian is the same,
within the error of photometric test, for all incandescent lamps
of the same type of filament, usually the distribution curve of
one meridian is measured once for all, therefrom the ratio of
horizontal to mean spherical candle power, the so-called spherical
reduction factor, determined, and then in further photometric
tests of lamps of this type only the horizontal intensity meas-
ured, and from this, dividing by the spherical reduction factor,
the mean spherical intensity is derived. Thus, while with the
incandescent lamp the intensity varies in each meridian, and is
different in the different meridians, the mean spherical intensity
nevertheless is derived by a single photometric observation of
the horizontal intensity with rotating lamp: the rotation aver-
ages between the different meridians, and the spherical reduction
factor translates from horizontal to mean spherical intensity.
Reduction factors of incandescent lamps usually are between
0.75 and 0.80.
84. Far more difficult is the matter with arc lamps : in the ordi-
nary carbon arc lamp, the intensity also varies in the meridian,
and is different in the different meridians, but not with the
same regularity as in the incandescent lamp, and, further-
more, the intensity distribution between the different meridi-
ans, as well as, to a lesser extent, the total light flux of the
lamp, varies with the time. The arc is not steady and con-
stant in position, as the incandescent filament, but wanders,
and the light intensities on the side of the lamp, where the arc
happens to be, thus are greater than on the side away from the
arc. The meridians of maximum and of minimum intensity,
MEASUREMENT OF LIGHT AND RADIATION. 183
however, do not remain constant in position, but continuously
change with the wandering of the arc. Therefore, by measure-
ments in a single meridian, the distribution curve of maximum
and that of minimum intensity can be determined by waiting
during the observation for the arc to come around to the
side of the observer — maximum — and go to the opposite
side — minimum — intensity. Such curves are shown in Fig. 61.
FIG. 61.
This, however, carried out for every angle in the meridian,
makes arc-light photometry rather laborious, especially as
the total intensity pulsates with the time, and therefore a
considerable number of readings have to be taken in every
position.
Therefore, for arc light photometry, integrating photometers
are especially desirable, that is, photometers which, by a single
observation, determine — more or less accurately — the mean
spherical intensity; that is, the average intensity, in all directions.
With such an integrating photometer, by taking a number of
successive readings and averaging, so as to eliminate the varia-
tion of total intensity with the time, the mean spherical inten-
sity, and thus the total flux of light, can be derived more
rapidly.
Such an integrating photometer is the Matthews photometer.
It consists of a circle of inclined mirrors, which surround the
lamp and reflect the light in all — or, rather, a certain number
of — different angles into the photometer, and there the differ-
ent reflected beams are by absorption reduced in the proportion
184 RADIATION, LIGHT, AND ILLUMINATION.
of cos (f> and combined on the photometer screen. Obviously,
the Matthews photometer does not average the intensity in all
directions, but only in two meridians opposite to each other;
however, by averaging a number of successive readings, very
accurate results can be derived.
A method of averaging in all directions is based on a similar
principle as that by which the radiation from the interior of a
closed sphere of constant temperature was found to be black-
body radiation: if the lamp is located in the center of a closed
sphere (perforated only at the place where the photometer
enters) of perfectly white reflecting surface, then the light in-
tensity throughout the entire inner surface of the sphere is
uniform, and is the mean spherical intensity of illumination at
the distance of the radius of the sphere. The reason is : every
element of the interior of the sphere receives light directly from
the lamp, and also light reflected from all the other elements
of the sphere, so that the total light received at every element
of the sphere is the same, hence is the average illumination.
By enclosing the test lamp in the center of such a photometric
sphere of sufficient size, its mean spherical intensity thus can be
determined by a single reading. Such an arrangement has the
further advantage that it allows a direct measurement of mean
spherical intensity — or light flux — of such illuminants as the
mercury lamp, in which the radiator is of such extent that it
cannot be considered as a point without going to excessive
distances.
85. Photometrically, and in illuminating engineering, only
the mean spherical intensity — which represents the total flux
of light — and the distribution curve — which represents the
distribution of this light in space — are of importance. The
"horizontal intensity7' has been used as a conventional rating
of incandescent lamps, but is merely fictitious, as it does not
mean an actual average horizontal intensity, but the horizontal
intensity which the light flux of the lamp would give with the
standard mean spherical reduction factor, if the filament had
the standard shape.
Downward candle power and maximum candle power obvi-
ously have no meaning regarding the light flux of the lamp,
but merely represent a particular feature of the distribution
curve.
MEASUREMENT OF LIGHT AND RADIATION. 185
Hemispherical candle power is used to some extent, especially
abroad. It is a mixture between light flux and distribution
curve, and as it gives no information on the total light flux, nor
on the actual distribution curve, and may mislead to attribute
to the lamp a greater light flux than it possesses — by mistaking
it with mean spherical candle power — it has no excuse for exist-
ence, and should not be used.
LECTURE X.
LIGHT FLUX AND DISTRIBUTION.
86. The light flux of an illuminant is its total radiation
power, in physiological measure. It therefore is the useful
output of the illuminant, and the efficiency of an illuminant
thus is the ratio of the total light flux divided by the power
input.
In general, the distribution of the light flux throughout space
is not uniform, but the light-flux density is different in different
directions from an illuminant.
Unit light-flux density is the light-flux density which gives
the physiological effect of one candle at unit distance. The
unit of light flux, or the lumen, is the light flux passing through
unit surface at unit light-flux density. The unit of light inten-
sity, or one candle, thus gives, if the light-flux distribution is
uniform in all directions, unit flux density at unit distance from
the radiator, and thus gives a total flux of light of 4 it units, or
4 it lumens (since the area at unit distance from a point is the
surface of a sphere, or 4 it).
The unit of light intensity, or the candle power thus given,
with a radiator of uniform light-flux distribution, 4 x lumens of
light flux, and inversely, a radiator which gives 4 it lumens
of light flux, gives an intensity of one candle, if the intensity is
uniform in all directions, and, if the distribution of the intensity
is not uniform, the average or mean spherical intensity of the
radiator is one candle. Thus one mean spherical candle rep-
resents 4 it lumens of light flux, and very frequently the mean
spherical candle is used as representing the light flux: the light
flux is 4 TT times the mean spherical intensity, and the mean
spherical intensity is the total light flux divided by 4 it, regard-
less whether the light flux is uniformly distributed or not.
The total light flux of an illuminant is derived by the sum-
mation or integration of the intensities, that is, the flux den-
sities at unit distance, in all directions from the radiator.
186
LIGHT FLUX AND DISTRIBUTION. 187
The distribution of light flux or of intensity is never uniform,
and the investigation of intensity distribution of the light flux
thus necessary.
The distribution of the light intensity of an illuminant de-
pends upon the shape of the radiator and upon the objects
surrounding it; that is, the distribution of the light flux issuing
from the radiator depends on the shape of the radiator, but
is more or less modified by shadows cast by surrounding
objects, by refraction, diffraction, diffusion in surrounding
objects, etc.
The most common forms of radiators are the circular plane,
the straight line, that is, the cylinder, the circular line or circular
cylinder and combinations thereof.
87. Very frequently the intensity distribution of an illumi-
nant is symmetrical, or approximately symmetrical, around an
axis. This, for instance, is the case with the arc lamp, the
incandescent lamp, most flames, etc. If the distribution is
perfectly symmetrical around an axis, the distribution in space
is characterized by that in one meridian, that is, one plane pass-
ing through the axis. If the distribution is not symmetrical
around the axis, usually the space distribution is characterized
by the distribution curves in two meridians at right angles to
each other, the meridian of maximum and that of minimum
intensity, and the distribution in the equatorial plane, that is,
the plane at right angles to the axis.
Distribution curves are best represented in polar coordinates,
and the angle <f> counted from the axis towards the equator
(that is, complementary to the " latitude" in geography).
As most illuminants are used with their symmetry axis in
vertical direction, and the downward light is usually of greater
importance, it is convenient in plotting distribution curves to
choose the symmetry axis as vertical, and count the angle $
from the downward vertical towards the horizontal; that is,
the downward beam would be given by (f> = 0, the horizontal
beam by ^ = 90 deg., and the upward beam by <j> = 180 deg.
The usual representation of the light-flux distribution in po-
lar coordinates does not give a fair representation of the total
light flux, or the mean spherical intensity of the light source,
but on the contrary frequently is very misleading. When com-
paring different polar curves of intensity distribution, it is
188 RADIATION, LIGHT, AND ILLUMINATION.
impossible to avoid the impression of the area of the curve as
representative of the light flux. The area of the polar curve,
however, has no direct relation whatever to the total light flux,
that is, to the output of the illuminant, since the area depends
upon the square of the radii, and the light flux directly upon
the radii of the curve. Thus an illuminant of twice the inten-
sity, but the same flux distribution, gives a polar curve of four
times the area, and the latter gives the impression of a source
of light far more than twice as great as the former.
The meridian curves of intensity distribution are still more
misleading: the different angles of the curve correspond to
very different amounts of light flux: the horizontal intensity
(<£ = 90 deg.) covers a zone of 2 rn circumference, while the
intensity in any other direction (f> covers a zone of 2 rn sin <j>
circumference; that is, an area which is the smaller, the nearer
(f> is to 0 or 180 deg. ; the terminal intensity, upward or down-
ward, finally covers a point only, that is, gives no light flux.
As the result hereof, an illuminant giving maximum intensity
in the downward direction, and low intensity in the horizontal,
gives a much larger area of the polar curve than an illuminant
of the same or even a greater total light flux which has its
maximum intensity in the horizontal. Comparing, therefore,
illuminants of different distribution curves, it is practically
impossible not to be misled by the area of the polar curve, and
thus to overestimate the illuminant having maximum downward
intensity, and underestimate the illuminant having maximum
horizontal intensity.
The misleading nature of the polar curves of intensity dis-
tribution in the meridian is illustrated by the curves in Figs.
64 and 99: the three curves of Fig. 64 give the same total
light flux; that is, the same useful output; but 2 looks vastly
greater than 1 or 3, and 3 especially looks very small. Curves
0, 1, 2, 3, 4 in Fig. 99 give the same total light flux, and curve
5 gives only one tenth the light flux. To the eye, however, the
curve 4 gives the impression of a far more powerful illuminant
than the curve 1, and curve 5 appears practically equal, if not
larger than 1, while in reality it represents only one tenth the
light output of 1.
88. In an illuminant in which the distribution of intensity
is symmetrical around an axis, and thus can be represented
LIGHT FLUX AND DISTRIBUTION
189
by one meridian curve, the total light flux is calculated thus:
Let / = intensity at angle <f>
(counting the angle <j> from one pole over the equator to the
other pole).
This intensity covers a zone of the
sphere of unit radius of width d(j> and
angle <£,that is, a zone of radius (Fig. 62)
r = sin<£; thus surface
dA = 2 n sin
and the light flux in this zone therefore
is:
FIG. 62.
= 27r/sin<M^
hence, the total light flux :
<£ = 2 TT / /sin (f>d(/>.
Jo
CD
(2)
The light flux in the space from the downward direction </> = 0
to the angle <£ = fa against the vertical or symmetry axis, then
is
fc1 = 2 TT / sin <t>dfa (3)
*/0
and the light flux in a zone between the angles (j)1 and fa is
(4)
I. DISTRIBUTION CURVES OF RADIATION.
(1) Point, or Sphere, of Uniform Brilliancy.
In this case, the intensity distribution is uniform, and thus, if
/ = intensity of light, in candles,
<£= 4 nl = light flux, in lumens; (5)
or, inversely:
<I>
/ = -. (6)
The brilliancy of a radiator is the light-flux density at its sur-
face. Thus, with a luminous point of intensity /, the brilliancy
190
RADIATION, LIGHT, AND ILLUMINATION.
would be infinite; with a luminous sphere of uniform intensity
distribution, and of radius r, the brilliancy is
* 7 ' (7)
B =
,2 '
hence, inversely proportional to the square of the radius of the
spherical radiator.
(2) Circular Plane of Uniform Brilliancy.
89. Such radiators are, approximately, the incandescent tip
of the carbons in the (non-luminous) electric carbon arc, or
the luminous spot in the lime cylinder
of the lime light (hydro-oxygen flame),
etc.
Choosing the circular luminous plane
as horizontal direction, the intensity
distribution is symmetrical around the
vertical, the vertical direction thus can
be chosen as axis, and the angle <£
counted from the vertical upward. '
The intensity is a maximum 70, ver-
FlG- 63- tically downward, for <£ == 0.
In any other direction, under angle (f> against the vertical
(Fig. 63), the intensity is
/ = /0 cos <£, (8)
and is zero for
<£ = 90 deg.
The light flux issuing from the radiator below angle <f> is, by
(3):
hence, by (8) :
rsin (j) cos (f)d<f>
-I. /cos 2*
& I I
-/„{! -cos 24,},
(9)
LIGHT FLUX AND DISTRIBUTION. 191
and the total light flux, from (f> = 0 to <j> = 90 deg. = — , thus is :
ft
or
The brilliancy of the source of light is the total light flux
divided by the luminous area; or,
*
and, if r = radius of the luminous circle,
A = ;rr2,
and
-?'' 02)
or,
70 = r2£; (13)
that is, the same as in class (1).
Comparing (11) with (5), it thus follows that the total light flux
of such a radiator, for the same maximum intensity, is only one
quarter that of a radiator giving uniform intensity distribution
throughout space, or inversely, with such a downward distribution
of light, the maximum intensity is four times as great as it would
be with the same total light flux uniformly distributed through
space.
The flux distribution is a circle having its diameter from the
source of light downward. It is shown as 2 in Fig. 64, and
the concentric circle giving uniform intensity distribution of
the same total light flux is shown as 1.
(3) Hollow Circular Surface.
Such a radiator, for instance, is approximately the crater of the
positive carbon of the arc lamp.
As with such a radiator, as shown in section in Fig. 65, the
projection of the luminous area in any direction <f> is the same
192 RADIATION, LIGHT, AND ILLUMINATION.
FIG. 64.
FIG. 65.
FIG. 66.
LIGHT FLUX AND DISTRIBUTION. 193
as with the plane circular radiator (2), the same equations
apply.
(4) Rounded Circular Surface.
Such, for instance, is approximately the incandescent carbon
tip of the arc-lamp electrodes, when using carbons of sufficiently
small size, so that the entire tip becomes heated.
Assuming, in Fig. 66, the radiator as a segment of a sphere, and
let 2 aj = the angle subtending this segment, rl the radius of this
sphere.
For all directions <£, up to the angle co below the horizontal :
0< 0 <£-w ;
the projection of the spherical segment in Fig. 66 is the same as
that of a plane circle, and thus the intensity is given in class (1),
as:
i = 70 cos (/>.
In the direction, -- - co <<£<-, however, the intensity is
A 2i
greater, by the amount of light radiated by the projection Dyx,
and, in the horizontal direction, the intensity does not vanish,
but corresponds to the horizontal projection of the luminous
segment.
Above the horizontal, light still issues in the direction,
from the segment Buv, and only for - + co < <j> does the light
Zi
cease.
If r2 = radius of carbon, the radius of the luminous segment is
sin co'
the height of the segment is
h = rl (1 — cos co)
r2 (1 — cos co)
sin co
194 RADIATION, LIGHT, AND ILLUMINATION,
hence the surface of the segment, or the luminous area, is
A2 = 2 rjin
2 r227r (1 — cos w)
2r227r X 2 sin2
• 2 2
4 sin2 - cos -
Z 2
COS 2
(14)
Thus, if the luminous area is the same as in the plane circle
class (2), it must be:
TV2 7T
r2 = rcos~; (15)
and, if the brilliancy B is the same, the maximum intensity for
<t> = Ois
cos2 ; (16)
that is, the rounding off of the circular radiator, at constant bril-
liancy and constant luminous surface, decreases the maximum
intensity 70 by the factor cos2-, but increases the intensity within
the angle from co below to a> above the horizontal direc-
tion.
In Fig. 67 are plotted the distribution curves, for the same
brilliancy and the same area of the radiator, for a plane circular
radiator, as 1 ; a rounded circular radiator of angle co = 30 deg.
as 2, and a rounded circular radiator of angle a> = 60 deg.,
LIGHT FLUX AND DISTRIBUTION.
195
as 3. As seen, with increasing rounding, gradually more and
more light flux is shifted from the vertical into the horizontal
direction.
FIG. 67.
Straight Line or Cylindrical Radiator.
90. Such radiators are represented approximately by the lum-
inous arcs with vertical electrodes, by the mercury-arc tube,
by straight sections of
incandescent-lamp fila-
ments, etc.
The intensity distribu-
tion is symmetrical with
the radiator as axis.
The intensity is a max-
imum 70 at right angles
1,1 T i • FIG. 68.
to the radiator, or in
horizontal direction, <j> = 90 deg., when choosing the radiator as
vertical axis. At angle <£, the intensity is, Fig. 68,
I = /o sin 0, (17)
and is zero for </> = 0 and (f> = 180 deg., or in the vertical.
196 RADIATION, LIGHT, AND ILLUMINATION.
The light flux within angle <f> from the vertical is, by (4),
= 7r/0 f (l-co
«^o
hence, , A _ / . sin 2
and the total light flux for (f> = K is
* = »v.; (19)
or, inversely: ^_ ^ ? : (2Q)
and the radiating surface is
A = ^ (21)
where Z is the length; w the diameter of radiator. The bril-
liancy, therefore, is ^
(22)
may be called the linear maximum intensity, or, maximum inten-
sity per unit length.
Most of the light 'of a linear vertical radiator issues near the
horizontal, very little in downward and upward direction. Put-
ting <J>0 = J $, gives the angle <f>, which bisects the light flux :
sin 2 (f> n
* — =4'
and herefrom, by approximation, $ = 66 deg.; that is, half the
light flux issues within the narrow zone from 24 deg. below to
LIGHT FLUX AND DISTRIBUTION.
197
24 deg. above the horizontal, or in the space between a and a' in
Fig. 68.
It is interesting to compare the three radiators, (1), (2), and (5),
on the basis of equal maximum intensity, and on the basis of
equal light flux, thus :
Light flux <£, at equal maximun
intensity /0
Maximum intensity 70, at equal
light flux $
Uniform.
47T/0
4
4^
1
Circle. Cylinder.
7T= 3.14
1=1.27
7T
As seen, at the same maximum intensity, the cylinder gives
nearly as much light flux as given by uniform distribution, that
is, its deficiency in intensity in the polar regions represents very
little light flux. The circular plane, however, gives only one
quarter as much light flux as uniform distribution.
With the same horizontal intensity of a cylindrical radiator,
as the vertical intensity of a circular plane, the former gives
TT = 3J4 times the flux of light.
In Fig. 64 the three distribution curves are shown for the same
total flux of light: curve 1 for uniform intensity, 2 for a plane
circle, and 3 for a straight cylinder as radiator.
(6) Circular Line or Cylinder.
In the spirals, loops or ovals of in-
candescent-lamp filaments, circular
radiators, or sections thereof, are met.
Let r = radius of the circular radi-
ator, w = diameter of the radiator
cylinder, shown in section in Fig. 69.
The intensity is a maximum in the
direction at right angle to the plane
of the circle.
The projection of the radiator in this direction of maximum
intensity, $ = 0, has the length: 2 TIT; and if, by (24) :
wB
69-
maximum linear intensity,
198 RADIATION, LIGHT, AND ILLUMINATION.
where B = brilliancy,
it is, IQ=27rrIQ'=2rwB. (25)
This is in the direction in which the projection of the radiator
is a circle of radius r, and thus circumference 2 TTT.
In any other direction </>, the projection of the radiator is an
ellipse, with r and r cos (f> as half axes, as seen from Fig. 69.
If I = the circumference of this ellipse, the intensity in the
direction <j> bears to the maximum intensity 70 the same ratio as
the circumference of the ellipse to that of the circle; that is,
I-It^—Ifl. (26)
2 nr
The circumference of an ellipse with the half axes a and c is
I = (a + c) n (1 + q),
I/a - c\2 1 /a - c\4 1 /a - c\8 W
4 \a + c) + 64 Va + c) + 256\a + c) + ' '
where
The ratio of the circumference of the ellipse to its maximum
diameter, y = — , is given in Table I, and plotted in Fig. 70,
w T
with the ratio of the half axes, that is, cos <p, as abscissas, and, in
Fig. 71, with angle <f> as abscissas.
TABLE I. — CIRCUMFERENCE OF ELLIPSE.
c
- — COS d>.
a
V = Tr-
f
V=ir-
1.0
1.571- s
0
1.571 = 5
2
2
0.9
.495
10
1.560
0.8
.418
20
1.525
0.7
.345
30
1.470
0.6
.278
40
1.390
0.5
.210
45
1.350
0.4
.150
50
1.305
0.3
.110
60
1.220
0.2
.055
70
1.120
0.1
.025
80
1.045
0
.000
90
1.000
LIGHT FLUX AND DISTRIBUTION.
199
\
y -
1.5
1.4
1.3
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
\
X
N
X
X.
X
^
\
^
C(
£
minimum p,
mayimu/Ti
imet
erof
Ellii
sis
0
I 0
,i.
4 0*5 0
6 0
7 0
8 0
9
-^v
1.5
1.4
1.3
1.2
1.1
1.0
0.0
0.8
0.7
0.6
0.5
0.4
0.3
0.2
'0.1
^
\
\
\
^
x
^
V,
1
2
Angle^Deglrees
0 3.0 40 1?0 6
0 *i
tt f
>
FIG. 70.
FIG. 71.
In Fig. 72 is plotted the intensity distribution in the meridian
of such a circular radiator.
This shows a maximum 70 in the
vertical, and a minimum ^= — 70
7T
in the horizontal.
Theoretically, exactly in the
horizontal, <f> = 90 deg., the in-
tensity should be ~, as one half
ft
of the circle shades the other
half. In most cases of such circular
radiators, sections of incandescent-
lamp filaments, w is so small com-
pared with r, that it is practically
impossible to have the radiator
perfectly in one plane, as would be
required for one half to shade the
other half.
(7) Single-Loop Filament.
FIG. 72.
200
RADIATION, LIGHT, AND ILLUMINATION.
92. As an illustration of the use of the distribution curves
of different typical forms of radiators, the distribution curves
of a single-loop incandescent-lamp filament may be calcu-
lated.
Such a filament consists of two straight sides, joined by a half
circle, as shown in Fig. 73.
The distribution of in-
tensity is not symmetrical
around any axis, but ap-
proximately so around the
axis Z in Fig. 73.
The meridian of maxi-
mum intensity is the plane
YZ, at right angles to the
plane of the filament ; the
meridian of minimum in-
tensity is the plane of the
filament, XZ, and the
least variation of intensity
occurs in the equatorial
plane XY. The distribu-
tion curves in all three of
.these planes are required.
Assuming the straight
sides as of a length equal
to twice the diameter of
the loop, or of length 4 r,
where r = radius of the half circle.
As it is impossible to produce and maintain such a filament
perfectly in one plane, we assume, as average deviation of the two
straight sides A and B of Fig. 73 from the vertical, an angle of
10 deg.
The intensity distribution of the straight sides A and B in any
meridian plane thus is that of a straight radiator, (5), at an
angle of 10 deg. against the vertical.
Let // = maximum intensity per unit length. Then the
meridianal distribution of the sides A + B is :
FIG. 73.
7 = 4 r/
sn
+ 10°) + sin (0 - 10°) }
(28)
Hereto in the meridian of maximum intensity is added the light
LIGHT FLUX AND DISTRIBUTION. 201
intensity produced by a half circle of radius r, (6); that is,
'2 = £-' (29)
where I is the circumference of the ellipse which projects the
circle of radius r, under angle <£, and is given by Table I and
Figs. 70 and 71.
FIG. 74.
In the meridian of minimum intensity, the light intensity 73
produced by the projection of the half circle in its own plane,
under angle (f>, is added to the intensity 7t. This projection is,
by Fig. 73,
c = r (1 + cos <£), (30)
and thus 73 = c70'
= rIQ' (1 + cos 0). (31)
In the equatorial plane, the intensity, due to the straight sides
A + B, is constant, and is that of a straight radiator under angle
10 deg. from the direction of maximum intensity; hence is
70 = 8 rI0' cos 10°. (32)
To this is added the intensity produced by the half circle of
radius r, that is, 72; hence, in the meridian of maximum intensity,
7 = 7j + 72, Curve 1 of Fig. 74; in the meridian of minimum
202
RADIATION, LIGHT, AND ILLUMINATION.
intensity, / = 7X 4- 73, Curve 2 of Fig. 74 ; and in the equator,
7 = 70 + 72, Curve 3 of Fig. 74.
(8) In Table II are recorded the intensity distribution of the
different radiators discussed in the preceding paragraphs.
TABLE II.
Circular surface.
Single-loop filament.
*
Rounded by
Circular
Meridian of
Plane.
30 deg.
60 deg.
Max.
intensity.
Min.
intensity.
Equator.
0
7.00
6.50
5.25
3.14
1.70
1.70
5.51
10
6.88
6.40
5.18
3.12
1.73
1.68
5.50
20
6.57
6.12
4.94
3.05
2.47
2.35
5.46
30
6.05
5.63
4.56
2.94
3.19
2.97
5.41
40
5.35
4.98
4.07
2.78
3.84
3.53
5.33
50
4.50
4.19
3.55
2.61
4.41
4.02
5.24
60
3.50
3.25
3.01
2.44
4.88
4.41
5.16
70
2.39
2.31
2.44
2.24
5.23
4.70
5.06
80
1.21
1.47
1.90
2.09
5.44
4.88
4.98
90
0
0.75
1.37
2.00
5.51
4.94
4.94
100
0.39
1.00
110
0 09
0 07
120
0
0.04
130
0 02
140
0 005
150
0
77. SHADOWS.
93. The radiator of an illuminant can rarely be arranged so
that no opaque bodies exist in its field of light flux and obstruct
some light, that is, cast shadows. As the result of shadows, the
distribution of intensity of the illuminant differs more or less
from that of its radiator, and the total light flux is less.
The most common form of shadow is the round shadow sym-
metrical with the axis of the radiator, that is, the shadow of a
circular plane concentric with and at right angles to the sym-
metry axis of the illuminant. Such for instance are, approxi-
mately, the shadows cast by the base of the incandescent lamp,
by the top of the arc lamp, etc. Such also are the shadows of
LIGHT FLUX AND DISTRIBUTION.
203
the electrodes in the arc lamp in that most common case where
the electrodes are in line with each other.
As an example may be considered the effect of a symmetrical
circular shadow on the light flux and its distribution with a
circular plane and with a straight line as radiator.
(1) Circular Plane Opposite to Circular Plane of Radiator.
Shadow of negative carbon in front of the positive carbon
of the carbon arc.
In Fig. 75, let 2 r be the diameter of a circular plane radiator
(positive carbon) ; 2 rl
the diameter of the
plane, which casts a
shadow (negative car-
bon of the arc lamp);
and I the distance be-
tween the two.
Assume 70 as the
maximum intensity of
the light flux issuing
from the radiator AOB
(which is in downward
direction, hence com-
pletely or partly intercepted by the circle Afl^BJ. Then, the
intensity of the light flux from the radiator, in any direction $,
is, according to reasoning under heading I, class (2) ,
7 = /0cos0. (1)
In this direction <j>, the circle AlBl projects on the plane AB
as a circle A2B2) with radius rv and the center 02 of this circle
has from the center 0 of the radiator the distance
FIG. 75.
a = 00
tan
(2)
If now the projected circle 02 overlaps with the radiator circle
Ov the area S of overlap, shown shaded in Fig. 76, is cut out from
the radiator by the shadow, and the light flux in the direction <j>
thus reduced from that of the complete radiator surface, Trr2,
to that of the radiator surface minus the shaded part S, that is,
xr2-S, or in the proportion
2* -S
s
r'x
(3)
204 RADIATION, LIGHT, AND ILLUMINATION.
and the intensity of the remaining light flux, in the direction <f>,
thus is I = I0q cos <£. (4)
If the distance, a, between the circles 0 and 02 is greater than
the sum of radii, I tan (j> > r + r17 the circles 0 and 02 do not
overlap, and in that direction no shadow is cast.
The light intensity thus is reduced by the shadow of the lower
carbon only for those angles <j> which are smaller than the angle
<t>i given by r + r
~--A (5)
In the direction in which <£ is smaller than the angle,
r. — r
tan ^2 = ~ — > (6)
and the shadow 02 thus covers the entire radiator 0, no light
issues, but the radiator is completely shaded. This can occur
only if rt>r, and if this is the case, a circular area below the
radiator receives no light.
If fj= r, the intensity becomes zero only in the direction
<j> = 0; and if 7\ < r, the light in the downward direction is merely
reduced, but nowhere completely extinguished.
The shaded area of the radiator consists of two segments,
of the respective radii r and r1 : S = D + Dr
Let 2 co = angle subtending segment D and 2 co^ = angle
subtending segment Dv and denoting the width of the segments
thus
w = AC,
and the total width of the shaded area is
p = AB2 = w + w,. (7)
From Fig. 76,
a = 002 = OA + J~02 - AB2
= r + r, - p;
or,
p = r + rt - a;
hence, by (2),
p = r + TI - tan 0. (8)
LIGHT FLUX AND DISTRIBUTION.
In A 02EO,
205
sin <
sin
sin (
r .
- sm aj,
and
hence,
Furthermore,
S = D + D,
and, by (3),
(9)
(10)
(ID
(12)
(13)
(14)
(15)
(16)
For different values of w the
values of to wt p D D, S q
are calculated from equations (10) (11) (12) (13) (14) (15) (16)
and then q plotted as function of p in Fig. 78.
206
RADIATION, LIGHT, AND ILLUMINATION.
From equation (8) then follows, for every value of <£, the cor-
responding value of p, herefrom the value of q and by (4) the
value of /.
fl
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
*>
N
^
N
^
\
^
\
>
\\s
^V
in
\
\
\I
v
I\
\
\
V
\n
P =
5
o
1 0
2 0
3 0
t 0
5 0
6 0
7 0
8 0
^
FIG. 78.
94. In Table III are given
the values of p and q for the
ratio of radii :
^- = 2.0; 1.0; 0.7,
corresponding to a shadow sec-
tion equal to 4 times, 1 times,
and 0.5 times the section of the
radiator.
These are plotted as curves
I, II, III, in Fig. 78.
TABLE III.
P'
r-l=2.
r
3-1.
r
TI
r
= 0.7.
I.
II.
III.
IV.
0
1.000
1.000
1.000
0 96
0.1
0.962
0.964
0.968
0.2
0.885
0.895
0.910
0.3
0.785
0.810
0.835
0.4
0.675
0.715
0.748
0.5
0.6
0 65
0.560
0.435
0.615
0.500
0.660
0.575
0 532
0.660
0.569
0 520
0.7
0 71
0.308
0.380
0.502
0 500
0.477
0.8
0.85
0.183
0.255
0.500
0.386
0 340
0.9
0.070
0 127
0 500
0.95
0.028
0 063
1.0
0
0
0 500
t
If — < 1, the curve III represents the effective light-living
area only up to the values of p, where wl = rv but beyond this
value, at least in the application to the shadow cast by the
LIGHT FLUX AND DISTRIBUTION. 207
negative carbon of the arc lamp, the shaded area is not merely
the circle O/, but also the area shown shaded in Fig. 77,
which is shaded by the shadow cast by the sides of the lower
electrodes.
From the value p, which corresponds to wl = rv the area S
then increases by 2^ (p-p)', hence, if S'= shaded area for
p = p'j for any value of p>pv
and q = l ;- ^j^. (17)
XT nr2
This is shown in Table III and in Fig. 78 as curve IV.
Such curves of intensity of a plane circular radiator of radius
r, shaded by a concentric circular shade of radius rl at distance I
[corresponding to a diameter of positive carbon 2 r, of negative
carbon 2 ri; and an arc length Z], are given in Figs. 79 to 82,
and the numerical values given in Table IV.
r I
Fig. 79 gives the curves for - = 2, and the arc lengths, — =
0.25; 0.5; 1.0; 2.0, as curves I, II, III, IV. Fig. 80 gives the
r 2r
curves for - = 1, and the arc lengths, —= 0.25; 0.5; 1.0; 2.0,
r I r
as curves I, II, III, IV. Fig. 81 gives the curves for - = 0.7,
I r
and the arc lengths, — - = 0.25; 0.5; 1.0; 2.0, as curves I, II, III,
IV. In Fig. 82 are shown, for comparison, the intensity curves
for
i-2; 2-r=2'asL
5-1; 1-1, as II.
^ = 0.7; ~=0.5, as III.
T £ T
As seen from Fig. 82, a larger shade at greater distance, I,
gives approximately the same light flux and a similar distribu-
tion, but gives a much sharper edge of the shadow, while a smaller
208 RADIATION, LIGHT, AND ILLUMINATION.
V////A W/\ v////\
FIG. 81.
FIG. 82.
LIGHT FLUX AND DISTRIBUTION.
209
j
0
co
i b- t^. o i^ o co o 10 10 o co »o o o »o o
»-i o o <o t^ 10 co o t- •* o 10 o •<*< r^ o
o »-• c<i M co ^ >o «o eo r^. oo oo oi o> o> d
11
S 3
II
0
• ! !! t^.^t"o co»oo io»oo «oo»oo
O-. •• cococo »o^co i-io>t^ eoo»oo
. I . '. o i-i <M co •* »o «o <o t>. od o» o> d
I C
~l«
IO
<M ^ CO 00 OS 0 •-< S 0
fl
0
O- OT-HCNCO-*»Ot>-oOOSO
8
10
CO
!! l!i ! 03COOOOOOOO
. . . . . . CO IO Tj< CO CM O
o
o • • • • • . o o CM •«* co oo o
T-H
o
t^OlO O5O5i— I t^C<lt-- i— 1 ^f t-» OC^C^ COt^-C3i
(N
CO »O CO t^ 00 OS 00 00 t^ t^ CO IO »O ^ CO CO rH O O
H«
0
t^-*o t^coos -*oot^ ^nrt<t^ o«MTt< cot^os
CO^lO tOCOCO t^t>»t^ t^CO>O »O^CO M i— I O O
t>I
d
»0
0
t^^H-^ cOOSi-H CO-^iO i-^CO*O o<N-rt< COt^OS
co-^Tfi T^T»<»O loioio io»oio iri^co co»-ioo
Cl u
IO
co
10 »o
t^oso I-I<MCO CO<NT-I ^HOOS coioco cot^os
i?
o
COCO'* -^Tt<Tl< rt<"*^ -«*<TJ<CO COCOCO <M'-"OO
13
o
QOCO ^OCO CDOSCO b-CO-^ OCO(M OS-*t^
i— I CO COOOOO CO >— I CO O^ft^ OCMrfrl »Ot^QO
a
II
CO
OC^-* COt>-00 OOOOt^ t^-COO >OTt<CO CM»-IOO
<o_
N
-IS
O
COOS 00 t>- if* CO IO O t^ CO -* O CO CO OS •«*< t>-
O--H CN(M(M OCO<M O^t^ OCN-* *Ot^OO
.1
"3
*""*
O>-i<N COTt<iO coiOIr^ t^eoiO lO-^CO CO»-iC>O
2
3
a
II
*TI v.
»o
d
COOO -^COOO t^OO OO<M iOCO(M OS-^t^
»0 0 CO ^H CO 1-H CO rH T*H CO t«- t- <M ^ »0 t>- 00
OOi-< »-iCS|<M COCO-* -«^-^TJ< -«t*TjIcO COi-HOO
1
A
iO
co
»O i— I t^»OCO COOCO t^COt^. COt^CO lO^t»
CN >0 1^ 0 CO 10 00 0 (N Tt< »0 t>-t^t>. 10^.00
J3
3
o
OOO O«-l<-l r-i»-iCN COCMCO COCOCO CO^-iOO
i
0
CO ^H -«** CO OS t^ >-irt<l^ 0 CO -«*< COt^OS
ii
CO
O -O O CO Tj« CO t>- b, t^ CO >O U5 T*I CO CO ^i O O*
„ 1 V-
IN
O
«O »O 00 O OS CO o CO •** CO t- OS
1—1
O- O OT-ICO Tt*^iO lO-^CO CO«-«OO
c4
11
•Tl t-
. . . . . . . . - —
»o
CO
i-i co co t^ o»
0
O • • ... ... ... OOO i-i ,-H O O
•s
88JS8Q
•e-
o 10 o »o o »o o m o to o »o o 10 o 10 o »o o
ri t-HCOCO COCO-* ^IO«O COcOt^ t^OOOOOS
210 RADIATION, LIGHT, AND ILLUMINATION.
shade at shorter distance, III, gives a far broader half shadow,
which extends even to the vertical direction.
This is illustrated by the distribution of the open arc and the
enclosed arc in clear globes — that is, without means of diffrac-
tion or diffusion. In the enclosed arc the distance between the
electrodes, I, is made larger, since the ratio of radii — is greater,
as due to the smaller current the diameter of the radiator, 2 r,
is smaller than in the open arc. The enclosed arc has a much
sharper edge of the shadow, that is, narrower half shadow, than
the open arc, thus requiring means of diffusion of the light even
more than the open arc.
Where the shade which casts the shadow is rounded, the dis-
tribution curve is somewhat modified by similar considerations,
as have been discussed under headings I, class (4). This is fre-
quently the case where the shadow is cast by the electrodes of an
arc, and especially so in the carbon arc, in which the negative
electrode — which casts the shadow — is more or less rounded
by combustion.
(2) Circular Plane Concentric with the End of Linear
Radiator.
95. This condition is approximately realized by the shadows
of the electrodes of a luminous arc with vertical electrodes.
Let, in Fig. 83, 2 r1 = diameter of the
lower electrode, I = length of the linear-
radiator, and 2 w the diameter of the radiator.
Neglecting first the diameter 2 w of the radi-
ator, the part of the radiator which, in the
direction <£, is shaded, is
s = r, cot <£, (18)
and the reduction factor of the light, or the
ratio, by which the intensity of light flux of
the radiator proper (heading I, class (5)),
/ = 70 sin 0, has to be multiplied, is
= 1 - COt <£, (20)
LIGHT FLUX AND DISTRIBUTION.
211
and the light intensity in the direction <£ thus is
/= qIQ sin <J)
= /0 ( 1 — j- cot (f> J sin ^
r / • ri
= /0 (sin $ — j cos
For values of 0 less than fa, where.
tan
T
-1 ,
(21)
(22)
the light flux is zero, that is, complete shadow would exist if there
were no diffusion, etc.
If we now consider the diameter, 2 w, of the radiator, we get
the same distribution of intensity, except in the angle
where fa' and fa' is given by
tan fa' = -*-
w
and tan fa" = -1— —
L
In this narrow angle the light flux fades from the value which it
has at fa" — and which is the same as given by equation (21) —
to 0 at fa', while, when neglecting 2w, the intensity would
become zero at fa by equations (22) and (21).
As illustrations are plotted in Fig. 84 and recorded in Table IV,
FIG. 84.
212 RADIATION, LIGHT, AND ILLUMINATION.
the distribution of light flux for— =0.25; 0.5; 1; 2, as curves I,
^ri
II, III, IV, corresponding to an arc length equal to J, J, 1 and
2 times the electrode diameter.
777. REFLECTION.
96. As rarely the distribution of intensity and the brilliancy
of the radiator are such as desired, reflection, diffraction, and
diffusion are used to a considerable extent to modify the distribu-
tion curve and the brilliancy of the radiator.
Reflection may be irregular or regular reflection. In irregular
reflection, the light impinging on the reflector is thrown back
irregularly in all directions, while in regular reflection the light
is reflected under the same angle under which it impinges on the
reflector. The former is illustrated by a piece of chalk or other
dull white body, the latter by the mirror.
A. Irregular Reflection.
Irregular reflection is used in indirect lighting to secure dif-
fusion and low intrinsic brilliancy of the light source by throw-
ing the direct light against the ceiling and illuminating by the
light reflected from white or light colored ceilings. In some
luminous arcs, the so-called flame carbon arc lamps, irregular
reflection is used to direct most of the light downward by
using a small circular reflector — usually hollow — immediately
above the arc, the so-called " economizer." In this case the
smoke produced by the arc largely deposits on the reflector
and thereby maintains it of dull white color, the deposit of most
flame carbons being calcium fluoride and oxide and thus white.
In irregular reflection, the reflector is a secondary radiator;
that is, if <$! = that part of the flux of light of the main radiator
which is intercepted by the reflector, and a = albedo of the
reflector (that is, the ratio of reflected
light to impinging light, or the "ef-
ficiency of the reflector"), the radiator
is a generator of the light flux a$r
As an example may be discussed
the intensity distribution of a vertical
FlG- 85- luminous arc L having a circular
(irregular) reflector R immediately above the arc, as shown in
Fig. 85. Let 2 aj = angle subtended by the reflector R from
LIGHT FLUX AND DISTRIBUTION. 213
the base of the arc, I the (vertical) length of the arc. The
radius of the reflector then is rl = I tan co, and the light flux
intercepted by the reflector is calculated in the manner as dis-
cussed under heading II, Class (2) ; that is, if 70 is the maximum
or horizontal intensity of the arc L, the intensity in the direc-
tion (180 deg. - <£) will be
7 = 70 sin <£. (1)
The reflector then intercepts the entire light flux issuing from
the radiator L between 180 deg. and 180 — co, and the part q of
the light flux issuing between 180 — co and 90 deg., which is
given by
r, cot (180 - </>) .A
q = - - — - — = tan co cot <£; (2)
i
hence, the light flux intensity which is intercepted by the reflec-
tor is
A = ?/o sin *
= 70 tan co cos <£, (3)
and the light intensity issuing into space from the main radiator
in this angle, - < <£< (180 - co), is
% sn
= 70 (sin $ — tan co cos (/>). (4)
Therefore the light flux intercepted by the reflector within the
angle (f> = 0 to ^> = co (or rather, <f> = 180 deg. to <f> = 180 — co) is
within the angle <£ = &> to </> = - is
$/' = 2 ^70 / g sin2 (j>d(j> = 2 nI0 tan o> / cos ^ sin
I + cos 2
7 sin 2 co
(5)
214 RADIATION, LIGHT, AND ILLUMINATION.
and therefore the total light flux intercepted by the reflector is
*1 * */ + ^l" = <">
and the reflected light flux, or light flux issuing from the reflector
as secondary radiator, is
4>2 = a^1 = xIQaco, (6)
where a = albedo.
As the reflector is a plane circular radiator, its maximum
intensity is in the downward direction, and is given under head-
ing I, class (2), as ^
V = - = /o«", (7)
71
and herefrom follows the intensity of radiation of the secondary
radiator in any direction <£,
r - /0" cos <£
= 70 aw cos 0. (8)
The total intensity of radiation of main radiator and reflector
or secondary radiator combined, in the lower hemisphere, or
for 0 < (j> < -j is
Zi
/ = /' + /" = /o (gin 0 + aaj cos <£); (9)
and in the upper hemisphere light flux issues only under the
angle - < $ < K — tu, and is
Zi
I = I' = 70 (sin ^ - tan w cos 0). (10)
FIG. 86.
For to = 75 deg. = and a = 0.7, the intensity distribution
12
is plotted in Fig. 86 and given in Table V. The distribution
LIGHT FLUX AND DISTRIBUTION.
215
curve is of the type characteristic of most flame carbon arc
lamps.
Substituting the numerical values in
(9) gives
and in (10) gives
7 = 70 (sin $ + 0.92 cos
7 = 70 (sin $ - 3.73 cos
TABLE V.
Regular: a = 0.6.
<!>.
Irregular reflection.
a = 0.7.
<a = 75 deg.
Regular reflection,
a = 0.7.
tal = 60 deg.
w2 = 85 deg.
Irregular: a' = 0.1.
&<! = 60 deg.
to2 = 85 deg.
2r.
— 1=1.
I
0
3.68
0
0.18
10
4.32
0.70
0.17
20
4.83
1.47
0.16
27
0 16
30
5.19
2.00
0.42
35
0 80
40
5.39
2.57
1.19
45
1 54
50
5.44
3.06
1.89
55
2 23
60
5.46
3.46
2.55
65
4.11
3 27
70
5.02
4.74
3.97
75
4.82
5.32
4.62
80
4.58
5.86
5.26
85
4.30
6.34
5.86
87 5
5 18
4 93
90
4.00
4.00
4.00
92 5
2 00
2 00
95
2.68
0
0
100
1.34
105
0
B. Regular Reflection.
97. With regular reflection by a polished reflector or mirror
as used, for instance, in some forms of luminous arcs, the reflector
is represented by a second radiator, which has the same shape as
the main radiator and is its image with regard to the plane of the
reflector. If a is the albedo of the radiator and 70 the maximum
216
RADIATION, LIGHT, AND ILLUMINATION.
intensity of the main radiator, the maximum intensity of the
virtual or secondary radiator is a/0.
The reflector then cuts out of the light flux of the radiator
that part intercepted by it, and adds to the light flux that part
of the (virtual) light flux of the secondary radiator which passes
through the plane of the reflector.
As example may be considered the intensity distribution of a
vertical luminous arc of length Z, supplied with a circular ring-
shaped mirror reflector concentric with and in the plane of the
top of the arc. Let a)l be the angle subtended by the inner,
co2 the angle subtended by the outer edge of the reflector, from
FIG. 87.
the base of the arc, as diagrammatically illustrated in Fig. 87;
then the intensity of the light flux of the main radiator
for
is
and for
is
where, by (2),
7 = 70 sin
7T -
hence,
and is zero for
q2 = tan w2 cot
cos
(ID
(12)
(13)
(14)
7/ = 70 (sin c/) — tan
(f> > 7T - 0)r
All the light flux issuing from the main radiator between the
upper vertical and the angle wt (0 < <£ < 6^)
1' = 70 sin <f> (15)
is wasted by passing through the central hole in the reflector.
LIGHT FLUX AND DISTRIBUTION. 217
Of the light flux issuing between angle ^ and - from the upper
2i
vertical, the part f <ut < <£ < - j
7,-fc/oSin* (16)
is wasted by passing through the hole in the reflector.
Since, by (13),
ql = tan ^ cot <£, (17)
it is : /! = 70 tan wt cos <£, (18)
7T
for ^i < 9 < o •
z
All the light flux issuing between the upper vertical and the
angle w2,
7'=70sin<£, (19)
is received by the reflector, with the exception of that part which
passes through the hole in the reflector.
Of the light flux issuing between angle aj2 and - from the upper
Z
vertical, the part
72= q2i0sm<j>
= IQ tan a)2 cos (j>,
for*>2<(£<^ (20)
2i
is received by the reflector, with the exception of that part which
passes through the hole in the reflector.
The total light flux intensity reflected by the reflector, or the
useful light flux of the virtual or secondary radiator, thus is, if
a = albedo of the reflector,
Within the angle -><£ > aj2 from the upper vertical,
2
7"= a (I2 — 7X) = aIQ (tan co2— tan ajj cos <£; (21)
within the angle a)2 >(f> >a>l from the upper vertical,
I'" = a (P - 7J = «70 (sin <£ - tan ^ cos <£) ; (22)
and for ^ > <£ > 0,
/"" = a (/' - 7') = 0; (23) .
218 RADIATION, LIGHT, AND ILLUMINATION,
hence, the light intensity of the illuminant, consisting of vertical
radiator and ring-shaped mirror reflector, for
0 < 0 < Wj is
7=70sin<£; (24)
for Wj< <j>< ^2 is
/= /'+ i"' = /o { (1 + a) sin <f> - a tan ^ cos <£) } ; (25
for
I = P + I" = 70 { sin <j> + a (tan w2 — tan w^ cos <£ } ; (26)
for
and for
7 -= 7/ = 70 (sin <f> — tan a>2 cos <£),
7 = 0.
17 n
(27)
For ^= 60° = , ^2 = 85°= — , and albedo a= 0.7, the in-
O OU
tensity distribution is plotted in Fig. 88 and recorded in
Table V.
FIG. 88.
Substituting the numerical values in the foregoing, we have:
(24) 7 = 70sin<£,
(25) 7 = 70 (1.7 sin $ - 1.21 cos <£),
(26) 7 = 70 (sin <£ + 6.79 cos 0),
(27) 7 = 70 (sin 0 - 11.43 cos <£).
98. As it is difficult to produce and maintain completely
regular reflection, usually some irregular reflection is superim-
posed upon the regular reflection.
For the irregular reflection, the reflector is a horizontal plane
radiator.
LIGHT FLUX AND DISTRIBUTION. 219
The light flux reflected by a plane circular reflector subtending
angles co1 to co2, by (6), is
$.,= */„ a' K L"i), (28)
where a' is the albedo of irregular reflection.
This light flux gives in the lower hemisphere the maximum
intensity for </> = 0 as
7." - 70a' (o,2 - a,,), (29)
and thus the intensity of the irregularly reflected light in the
direction < is
72 = /0" cos
- wj cos (£, (30)
and this intensity thus adds to that given by equations (24) to
(27) in the preceding.
If some light is obstructed by the shadow of the lower elec-
trode, then the light intensity of the main radiator, /', in the
lower hemisphere within the angle fa < (/> < - > is reduced to
2
(31)
and becomes zero for </> <</>,, where tan <£t == y as discussed
I/
under heading II, class (2), equations (21), (22), where r{ is the
radius of the lower electrode.
Thus, with a linear radiator of length I, a diameter of the
lower electrode of 2 rv a ring-shaped mirror reflector subtending,
from the base of the arc, the angles ^ and w2, and of the albedo
of regular reflection a and the albedo of irregular reflection a',
the light intensity distribution within is 0 < (f> < (j>v
I = //(^2- Wl)cos^; (32)
within (f>1 < (/> < Wj is
I = 70 (sin £+fy K - ^) -- ^J cos ^; (33)
within ^ < (j> < a>2 is
/ = /0 (1 + a) sin (/> + \a (co2 - ^) - atan^ -j lcos(/)|; (34)
220 RADIATION, LIGHT, AND ILLUMINATION.
within toy -
7T .
<21S
Jsin (j>+\ a (tan a)2- tan w^) + a' (to2-u^ - ~
cos
within
and within
I = I0 (sin $ — tan a>2 cos <£),
K — to2 < </> < n is
/ = 0.
(35)
(36)
FIG. 89.
The distribution curve of such an illuminant is plotted in
Fig. 89 and recorded in Table V for the values
^= 60 deg. = ; co2 = 85 deg. =-r',
a =0.60; a'= 0.10,
and
I
1.
Substituting the numerical values in the foregoing equations
this gives ^ = 27 deg.
(32) 7 = 0.044 70 cos </>,
(33) 7 = 70 (sin <j> - 0.456 cos <£),
(34) 7 = 70 (1.6 sin <£ - 1.495 cos <£),
(35) 7 = 70 (sin <j> + 5.364 cos <£),
(36) 7 = 70 (sin <j> - 11.43 cos <j>).
FIG. 90.
As comparison is given in Fig. 90 the distribution curve of
the magnetite arc, which is designed of the type of Fig. 89
for the purpose of giving more nearly uniform illumination in
street lighting.
LIGHT FLUX AND DISTRIBUTION. 221
IV. DIFFRACTION, DIFFUSION, AND REFRACTION.
99. Many radiators are of too high a brilliancy to permit
their use directly in the field of vision when reasonably good
illumination is desired. A reduction of the brilliancy of the
illuminant by increasing the size of the virtual radiator thus
becomes necessary. This is accomplished by surrounding the
radiator by a diffracting, diffusing, or prismatically refracting
envelope.
Diffraction is given by a frosted glass envelope, as a sand
blasted or etched globe; diffusion by an opal or milk-glass
globe. The nature of both phenomena is different to a consider-
able extent, and a frosted globe and an opal globe thus are not
equivalent in their action on the distribution of the light flux.
This may be illustrated by Fig. 91.
Let, in Fig. 91, 1A, R represent the light-giving radiator,
for simplicity assumed as a point, and G represent a diffracting
sheet, as a plate of ground glass. A beam of light, C, issuing
from the radiator R is, in traversing the diffracting sheet G,
scattered over an angle, that is, issues as a bundle of beams D}
of approximately equal intensity in the middle and fading at
the edges '. The direction of the scattered beam of light D, that
is, its center line, is the same as the direction of the impinging
beam C, irrespective of the angle made by the diffracting sheet
with the direction of the beam.
Different is the effect of diffusion, as by a sheet of opal glass,
shown as G in Fig. 91, IB. Here the main beam of light G
passes through, as C', without scattering or change of direction,
but with very greatly reduced intensity; usually also with a
change of color to dull red, due to the greater transparency of
opal glass for long waves. Most of the light, however, is irregu-
larly reflected in the opal glass, and the point or area at which
the beam C strikes the sheet G becomes a secondary radiator
and radiates the light with a distribution curve corresponding
to the shape of (2, that is, with a maximum intensity at right
angles to the plane of G, as illustrated in Fig. 91, 1 B.
A point P thus receives from a radiator R, enclosed by a diffract-
ing globe G, a pencil of light, as shown in Fig. 91, 2 A, and from
the point P the radiator appears as a ball of light, shown densely
shaded in 3 A, surrounded by a narrow zone of half light,
222
RADIATION, LIGHT, AND ILLUMINATION.
shown lightly shaded, and in the interior of a non-luminous or
faintly luminous envelope.
If the radiator R is enclosed by a diffusing globe, Fig. 91, B2,
the point P receives light from all points of the envelope G as
FIG. 91.
3-B
secondary radiator, and a ray of direct light from the radiator R.
From the point P the entire globe G thus appears luminous, and
through it shows faintly the radiating point R, as sketched in
3B.
An incandescent-lamp filament in an opal globe thus is clearly
LIGHT FLUX AND DISTRIBUTION.
223
but faintly visible, surrounded by a brightly luminous globe,
while an incandescent filament in a frosted globe appears as a
ball of light surrounded by a non-luminous or faintly luminous
globe, but the outline of the filament is not visible.
100. The distribution of light flux thus essentially depends
on the shape of the diffusing envelope, but does not much depend
on the shape of the diffracting envelope; that is, a diffracting
envelope leaves the distribution curve of the radiator essentially
unchanged, and merely smooths it out by averaging the light flux
over a narrow range of angles, while a diffusing envelope entirely
changes the distribution curve by substituting the diffusing globe
as secondary radiator, and leaves only for a small part of the light
- that of the direct beam C' — the intensity distribution of the
primary radiator unchanged.
Thus, for a straight vertical cylindrical envelope surrounding
a radiator giving the distribution curve shown in Fig. 92, curve I,
FIG. 92.
the distribution curve is changed by diffraction (frosted en-
velope), to that shown in Fig. 92, curve II, but changed to that
shown by Fig. 92, curve III, by diffusion (opal envelope). The
latter consists of a curve due to the transmitted light and of the
same shape as I, and a curve due to the diffused light, or light
coming from the envelope as secondary radiator. The latter is
the distribution curve of a vertical cylindrical radiator, as dis-
cussed under heading I, class (5).
The shape of a diffusing envelope thus is of essential importance
224
RADIATION, LIGHT, AND ILLUMINATION.
for the distribution of the light intensity, while the shape of the
diffracting envelope is of less importance.
TABLE VI.
f.
v
Clear globe.
v
Frosted globe.
V
Opal globe.
n
5
U
in
5
1U
20
6
8
11
2*5
7
12
m9
30
9
18
17
35
15
26
40
34
35
25
45
49.6
43
50
50.6
47.5
32
55
49.6
48
60
47.5
46
34.5
fi7
43
42
U 1
70
37
37
35
75
29
32
80
20
26
34
85
15
21
90
13.5
17
32
95
13
14
100
12.5
13
30.5
110
12
12
29.5
120
11
11
27
130
9
9
24
140
6
7
20
150
0
2
15
160
0
0
10
It is obvious that frosted glass does not perfectly represent
diffraction, but some diffusion occurs, especially if the frosting
is due to etching, less if due to sand-blasting. Opal glass also
does not give perfect diffusion, but, in the secondary radiation
issuing from it, the direction of the horizontal or impinging beam
slightly preponderates.
101. Regular or prismatic refraction also affords a means of
decreasing the brilliancy by increasing the size of the virtual
illummant, and at the same time permits the control of the
LIGHT FLUX AND DISTRIBUTION.
225
intensity distribution. It probably is the most efficient way,
as involving the least percentage of loss of light flux by absorp-
tion.
For instance, by surrounding the radiator R by a cylindrical
lens, as shown diagrammatically in Fig. 93, the rays of light may
^
FIG. 93.
be directed into the horizontal (or any other desired) direction,
and the entire lens then appears luminous, as virtual radiator.
Usually in this case, instead of a complete lens, individual sec-
tions thereof are used, as prisms, as shown in Fig. 94, and this
FIG. 94.
method of light control thus called "prismatic refraction," or,
where the light does not pass through, but is reflected and turned
back from the back of the prism, "prismatic reflection."
Such prismatically reflecting or refracting envelopes and shades
have found an extensive use.
LECTURE XI.
LIGHT INTENSITY AND ILLUMINATION.
A. INTENSITY CURVES FOR UNIFORM
ILLUMINATION.
102. The distribution of the light flux in space, and thus the
illumination, depends on the location of the light sources, and on
their distribution curves. The character of the required illumi-
nation depends on the purpose for which it is used: a general
illumination of low and approximately uniform intensity for street
lighting; a general illumination of uniform high intensity in
meeting rooms, etc.; a local illumination of fairly high intensity
at the reading-table, work bench, etc. ; or combinations thereof,
as, in domestic lighting, a general illumination of moderate inten-
sity, combined with a local illumination of high intensity. Even
the local illumination, however, within the illuminated area
usually should be as uniform as possible, and the study of the
requirements for producing uniformity of illumination either
throughout or over a limited area thus is one of the main prob-
lems of illuminating engineering.
The total intensity of illumination, i, at any point in space is
proportional to the light intensity, 7, of the beam reaching this
point, and inversely proportional to the square of the distance
I of the point from the effective center of the light source :
If the beam of light makes the angle <f> with the vertical
direction, the illumination, i, is thus in the direction <j>, the
horizontal illumination, that is, the illumination of a horizontal
plane (as the surface of a table), is
, 7cos< ,
ih = i cos 0 =
226
LIGHT INTENSITY AND ILLUMINATION. 227
and the vertical illumination, that is, the illumination of a vertical
plane (as the sides of a room), is
7 sin 0
iv = i sin <£ = — —!- •, (3)
If, then, in Fig. 95, L is a light source at a distance lv above
a horizontal plane P, then, for a point A at the horizontal dis-
FIG. 95.
tance lh from the lamp, L (that is, the distance lh from the point
B of the plane P, vertically below the lamp L), we have:
,
Lv
and the distance of the point A from the light is
cos
hence, the total illumination at point A is
. 7 cos2 () .
the horizontal illumination is
l
7 cos
and the vertical illumination is
. 7 cos2 <f> sin
(4)
(5)
(6)
(7)
(8)
where 7 is the intensity of the light source in the direc-
tion <j>.
Inversely, to produce a uniform total illumination, i0, on the
228 RADIATION, LIGHT, AND ILLUMINATION.
horizontal plane P, the intensity of the light source must vary
with the angle </> according to the equation (6) :
7" 1 2
(9)
or, if we denote by 70 the vertical, or downward, intensity of
the light source,
A, - V,2; (10)
hence,
7 = ^- (11)
gives the intensity distribution of the light source required to
produce uniform total illumination i0 on a horizontal plane be-
neath the light.
In the same manner follows from (7) and (8) :
To produce uniform horizontal illumination ihQ on a plane P
beneath the light source L, the intensity curve of the light source
is given by
cos3 </>
and, to produce uniform vertical illumination iVQ of objects in
the plane P beneath the light source L,
7- /0 (13)
cos" <p sin 0
Where the objects in the plane P which are to be illuminated
may have different shapes — as on a dining-table, work bench,
etc., uniformity of the total illumination, i, is desirable; where
all the objects which shall be illuminated are horizontal — as
the surface of a drafting-board — constancy of the horizontal
illumination ih is desirable, while where vertical objects are to be
illuminated — as, for instance, to read labels on bottles — con-
stancy of the vertical illumination iv is desirable.
By "horizontal illumination" ih is here understood the illumi-
nation of a horizontal plane, which is due to the vertical compo-
nent of the total light flux, while the "vertical illumination "
iv is the illumination of a vertical plane, due to the horizontal
component of the light flux.
LIGHT INTENSITY AND ILLUMINATION.
229
In Fig. 96, the intensity curves of the light source required
to give uniform total illumination i0 (11) in a horizontal plane
are plotted as curves I, II and III; the intensity distribution
for uniform horizontal illumination iho (12) is plotted as curve
IV, and the intensity distribution for uniform vertical illumina-
tion iVQ (13) in the horizontal plane beneath the light source
is plotted as curve V. For convenience, curves IV and V are
shown in the upper half of the diagram. The numerical values
for lv = 1 are recorded in Table I. With increasing angle $,
the required intensity increases very rapidly, and, as is obvious,
becomes infinite for (f> = 90 deg.
TABLE I.— (Figs. 95 and 96.)
UNIFORM DISTRIBUTION ILLUMINATION CURVES.
f.
COS (p.
Total.
1
Horizontal.
1
Vertical.
1
degrees.
cos2 <f>
cos3 <j>
sin ^ cos2 <f>
0
1
1
1
00
5
996
1.01
1.015
11.60
10
985
1.03
1.045
5.90
15
966
.07
1.11
4.30
20
940
.13
1.20
3.30
25
906
.22
1.35
2.88
30
866
.33
1.54
2.66
35
819
.49
1.82
2.59
40
766
.70
2.22
2.64
45
707
2.00
2.83
2.83
50
643
2.43
3.73
3.17
55
574
3.03
5.27
3.70
60
500
4.00
8.00
4.60
65
423
5.59
13.20
6.16
70
342
8.35
24.4
8.90
75
259
15.10
58.3
15.60
80
174
33.00
190.0
32.50
85
087
132.00
152.0
133.00
90
0
00
00
00
103. Therefore, in the problem, as it is usually met, of pro-
ducing uniform intensity i0 over a limited area, subtending angle
2 aj beneath the light source, the intensity of the light source
230 RADIATION, LIGHT, AND ILLUMINATION.
FIG. 96.
FIG. 97,
LIGHT INTENSITY AND ILLUMINATION. 231
should follow (11) for 0 < <f> < a>. Beyond <£ = a>, the intensity
may rapidly decrease to zero — as would be most economical, if
no light is required beyond the area subtended by angle 2 co.
This, for instance, is the case with the concentrated lighting of a
table, etc. However, the intensity beyond (f> = to may follow a
different curve, to satisfy some other requirements, for instance,
to produce uniform illumination in a vertical plane. Thus in
domestic lighting, for the general uniform illumination of a room
by a single illuminant, the intensity curve would follow equation
(11) up to the angle a> — if 2 w is the angle subtended by the floor
of the room from the light source — and for $ > cu the intensity
curve would follow the equation,
/ = -4-r, (14)
sin2 <j>
which gives uniform illumination in the vertical plane, that is, of
the walls of the room.
In Fig. 98 are shown intensity curves of a light source giving
uniform illumination in the horizontal plane beneath the lamp,
from 0 to CD, and the same uniform illumination in the vertical
plane from $ = a> to <j> = 90 deg., as diagrammatically shown in
Fig. 97; that is, uniform illumination of the floor of a room
and (approximately) its walls, by a lamp located in the center
of the ceiling, where cu is the (average) angle between the
vertical and the direction from the lamp to the edge of the
floor:
I for co = 30 deg.; or diameter of floor -f- height of walls =
2
2 tan 30 deg. = —==1.15.
II for co = 45 deg.; or diameter of floor -j- height of walls =
2 tan 45 deg. = 2.
III for aj = 60 deg.; or diameter of floor -H height of walls =
2 tan 60 deg. = 2 V3 = 3.46.
IV for a) = 75 deg.; or diameter of floor -f- height of walls =
2 tan 75 deg. = 7.46.
These curves are drawn for the same total flux of light in the
lower hemisphere, namely, 250 mean hemispherical candle power;
232 RADIATION, LIGHT, AND ILLUMINATION.
or, 1570 lumens. The vertical or downward intensities 70 are
in this case:
I: aj = 30 deg.; 70 = 428 cp.
II: cu = 45 deg.; 70 = 195 cp.
Ill: w = 60 deg.; 70 = 95 cp.
IV: aj = 75 deg.; 70 = 41.5 cp.
The values are recorded in Table II, in column I, for equal
downward candle power 70, and in column a, for equal light flux,
corresponding to 1 mean hemispherical candle power.
TABLE II. — (Figs. 97 to 99.) INTENSITY CURVES.
Uniform illumination from vertical <t> = 0 to <f> = « degrees from verti-
cal, and
(a) Uniform illumination (on vertical plane) from <f> = w to horizontal
0 = 90 deg.
(6) No illumination beyond <J> = w.
70 for unity illumination at 0 = 0.
a and 6 for mean hemispherical candle power 1, or 2 TT lumens.
<j>.
ca = 30 deg.
w = 45 deg.
a> = 60 deg.
to = 75 deg.
/0<
a.
6.
V
a.
b.
V
a.
b.
I0-
a.
6.
0
5
10
.00
.01
1.03
1.71
1.72
1.76
3.73
3.76
3.83
1.00
1.01
1.03
0.78
0.79
0.80
1.57
1.58
1.62
1.00
1.01
1.03
0.38
0.385
0.39
0.67
0.67
0.685
1.00
1.01
1.03
0.166
0.168
0.172
0.222
0.224
0.229
15
20
25
.07
.13
.17
1.83
1.93
2.00
3.98
4.20
4.35
1.07
1.13
1.22
0.83
0.88
0.95
1.68
1.77
1.99
1.07
1.13
1.22
0.41
0.43
0.465
0.71
0.75
0.81
1.07
1.13
1.22
0.178
0.188
0.203
0.237
0.251
0.271
30
35
40
1.20
1.01
0.81
2.05
1.73
1.38
4.47
3.57
2.24
1.33
1.49
1.70
1.03
1.16
1.32
2.08
2.33
2.66
1.33
1.49
1.70
0.51
0.57
0.65
0.89
0.99
1.13
1.33
1.49
1.70
0.221
0.248
0.283
0.295
0.331
0.377
45
50
55
0.67
0.57
0.50
1.14
0.98
0.85
0.57
0
1.80
1.70
1.49
1.40
1.32
1.16
2.85
2.50
1.10
2.00
2.43
3.03
0.76
0.93
1.16
1.34
1.62
2.02
2.00
2.43
3.03
0.333
0.405
0.504
0.445
0.540
0.672
60
65
70
0.44
0.41
0.38
0.75
0.70
0.65
1.33
1.22
1.13
1.03
0.95
0.88
0.31
0
3.60
3.51
3.39
1.37
1.34
1.29
2.40
2.00
0.80
4.00
5.59
8.35
0.665
0.930
1.39
0.887
1.24
1.86
75
80
85
0.36
0.34
0.34
0.61
0.58
0.58
1.07
1.03
1.01
0.83
0.80
0.79
3.21
3.09
3.03
1.22
1.18
1.16
0.20
0
12.80
12.40
12.10
2.13
2.07
2.02
2.85
2.11
0.67
90
0.33
0.57
1.00
0.78
3.00
1.14
12.00
2.00
0.11
LIGHT INTENSITY AND ILLUMINATION.
233
These curves in Fig. 98 consist of a middle branch, giving uni-
form floor illumination, and two side branches, giving uniform
side illumination, and are rounded off where the branches join.
FIG. 98.
Fig. 99 gives the intensity curves for the same angles, w = 30,
45, 60, and 75 deg., for uniform illumination only in the hori-
FIG. 99.
zontal plane beneath the lamp, but no illumination beyond
this; for <£ > a>, the light flux rapidly decreases.
The curves in Fig. 99 are also plotted for equal total light flux,
of 150 mean hemispherical candle power, or 940 lumens. The
234 RADIATION, LIGHT, AND ILLUMINATION.
curve, 0, giving (approximately) uniform illumination within an
angle of 20 deg., or for a> = 10 deg., is added to the set; this curve,
however, is plotted for one-tenth the light flux of the other
curves, 94 lumens, or 15 mean hemispherical candle power.
The vertical or downward intensities 70 are in this case, for
equal light flux of 940 lumens :
I: 'a> = 30 deg.; 70 = 500 cp.
II: a) = 45 deg.; 70 = 235 cp.
Ill: co = 60 deg.; 70 = 100 cp.
IV: aj = 75 deg.; 70 = 25 cp.
0: aj = 10 deg.; 70 = 7000 cp.
Fig. 99 best illustrates the misleading nature of the polar dia-
gram of light intensities. It is hard to realize from the appearance
of Fig. 99 that curves I, II, III and IV represent the same light
flux, and curve 0 one-tenth the light flux, that is, little more
than half the light flux of a 16-cp. lamp.
Curve 0, however, illustrates that enormous light intensities
can be produced with very little light flux, if the light flux is
concentrated into a sufficiently narrow beam. This explains
the enormous light intensities given by search-light beams: for
oj = 1 deg., or a concentration of the light flux into an angle of
2 deg. — which is about the angle of divergency of the beam of a
good search light —we would get 7 = 700,000 cp. in the beam,
with 15 mean hemispherical, or 7.5 mean spherical, candle power
light source; and a light source of 9000 mean spherical candle
power —a 160-ampere 60- volt arc —would thus, when concen-
trated into a search-light beam of 2 deg., have an intensity in the
beam of 70 = 210 million candle power, when allowing 75 per cent
loss of light flux, that is, assuming that only 25 per cent of the
light flux is concentrated in the beam.
The numerical values of Fig. 99 are given as b in Table II, for
equal light flux corresponding to 1 mean spherical candle power.
B. STREET ILLUMINATION BY ARCS.
104. To produce uniform illumination in a plane beneath
the illuminant, a certain intensity distribution curve is required,
as discussed in A ; for other problems of illumination, correspond-
ingly different intensity curves would be needed to give the
desired illumination.
LIGHT INTENSITY AND ILLUMINATION. 235
It is not feasible to produce economically any desired distribu-
tion curve of a given illuminant. Therefore, the problem of
illuminating engineering is to determine, from the purpose for
which the illumination is used, the required distribution of illu-
mination, and herefrom derive the intensity curve of the illumi-
nant which would give this illumination. Then from the existing
industrial illuminants, or rather from those which are available
for the particular purpose, that is selected whose intensity dis-
tribution curve approaches nearest to the requirements, and
from the actual intensity curve of this illuminant the illumination
which it would give is calculated, so as to determine how near it
fulfils the requirements.
The intensity curve of the illuminant, required to give the
desired illumination, depends on the location of the illuminant
and the number of illuminants used. Thus if, with a chosen
location and number of light sources, no industrial illuminant
can be found which approaches the desired intensity curve
sufficiently to give a fair approach to the desired illumination,
a different location, or different number of light sources would
have to be tried. Here, as in all engineering designs which
involve a large number of independent variables, judgment
based on experience must guide the selection. If so, practically
always some industrially available illuminant can be found
which sufficiently approaches the intensity curve required by
the desired illumination.
As example may be discussed the problem of street lighting.
This problem is : with a minimum expenditure of light flux-
that is, at minimum cost — to produce over the entire street a
sufficient illumination. This illumination may be fairly low,
and must be low, for economic reasons, where many miles of
streets in sparsely settled districts have to be illuminated.
This requires as nearly uniform illumination as possible, since
the minimum illumination must be sufficient to see by, and any
excess above this represents not only a waste of light flux, but,
if the excess is great, it reduces the effectiveness of the illumina-
tion at the places, where the intensity is lower, by the glare of
the spots of high illumination.
Uniformity of street illumination thus is of special importance
where the illumination must for economic reasons be low; while
in the centers of large cities, or in densely populated districts,
236
RADIATION, LIGHT, AND ILLUMINATION.
as European cities, the relatively small mileage of streets per
thousand inhabitants economically permits the use of far greater
light fluxes, and then uniformity, while still desirable, becomes
less essential.
TABLE III — (Figs 100 and 101.)
Intensity: 100 m. sph. cp.
Illumination: 200 m. sph. cp.; /„ = 20.
a.
6.
c.
a.
6.
c.
1
D. C.
D. C.
D. C.
D. C.
«c
enclosed
enclosed
Magnetite
Distance.
enclosed
enclosed
Magnetite
carbon
carbon
arc.
carbon
carbon
arc.
arc.
arc.
Clear
arc.
arc. .
Clear
Clear inner
Opal inner
globe.
Clear inner
Opal inner
globe.
globe.
globe.
globe.
globe.
4>.
7.
7.
7.
x = -•
i.
i.
t.
h
0
30
45
59
0
15
22.5
29.5X10~3
10
42
50
63
0.2
22
24.5
30.5
20
92
70
69
0.4
46
33.0
31.0
30
182
107
79
0.6
73
42.5
31.0
40
247
150
102
0.8
73
44.5
30.5
45
270
1.0
67
40.5
29.5
50
257
171
136
1.2
53
35.5
28.0
60
210
181
177
1.4
39
30.5
26.0
70
147
182
226
1.6
30.5
25.5
23.5
75
122
181
243
1.8
24.5
21.5
21.5
80
97
160
250
2.0
19.0
18.0
19.0
85
75
118
249
2.5
11.5
13.0
15.0
90
65
89
197
3.0
7.0
9.5
12.0
100
57
82
47
3.5
5.0
7.0
9.5
110
57
77
16
4.0
3.5
5.5
7.5
120
60
68
5.0
2.0
3.2
4.8
130
35
62
6.0
1.2
2.0
3.4
140
3
56
7.0
1.0
1.4
2.5
150
17
8.0
0.8
1 .0
2.0
9.0
0.5
0.8
1.7
10.0
0.4
0.6
1 1
15.0
0.2
0.3
0.5
20.0
0. 1
0. 1
0.3
25^0
0.1
Q.I
0^2
The arc, as the most economical illuminant, is mostly used
for street lighting. Fig. 100 gives the average intensity curves
LIGHT INTENSITY AND ILLUMINATION.
237
of three typical arcs for equal light flux of 200 mean spherical
candle power:
FIG. 100.
I. The direct-current enclosed carbon arc, with clear inner
globe: a curve of the character discussed in Fig. 82. II. The
direct-current enclosed carbon arc, with opal inner globe: a
0:20
III
1,60
1,00
0.4 0,2
08 0,4 06 08 10 12 It 16 18 20 22 24 26 28
FIG. 101.
curve of the character discussed in Fig. 92. III. The magnetite
arc or luminous arc, with clear globe: a curve of the character
discussed in Fig. 89. The numerical values are recorded in
Table III, per 100 mean spherical candle power.
238
RADIATION, LIGHT, AND ILLUMINATION.
Herefrom then follows, by equations (6) and (4), the (total)
intensity, i, in a horizontal plane beneath the lamp, at the
horizontal distance lh from the lamp, where lv is the height
of the lamp above this plane (the street).
These values of illumination, i, are plotted, with x = - as ab-
LV
scissas, in Fig. 101 and recorded in Table III for lv = 20, and
lamps of 200 mean spherical candle power.
105. With lamps placed at equal distances 4o, and equal
FIG. 102.
heights lv, as shown diagrammatically in Fig. 102, the illumina-
tion of any point A of the street surface is due to the light flux
of a number of lamps, and not only to the two lamps 1 and 2,
between which the point A is situated. As, however, the illumi-
nation rapidly decreases with the distance from the lamp, it is
sufficient to consider only the four lamps nearest to the point A.
The illumination of a point A of the street surface, at a horizon-
tal distance lh from a lamp, 1, then is:
i = ^ + i2 + ,; + ^ (15)
where iv iv is, i4 are the illumination due to the lamps 1, 2, 3, 4,
respectively.
I j
Let -r = P and ^==x; (16)
k lv
then the directions under which point A receives light are given
by:
tan fa = x,
tan fa = p — x,
tan fa = p + x,
tan fa = 2 p — x}
(17)
LIGHT INTENSITY AND ILLUMINATION.
239
and
1 lv2 cos2
/
V cos
cos
/4
cos
(18)
where Iv I2, 73, I4 are the intensities of the light source in the
respective directions <f>v <f>2,
100 120 110
FIGS. 103, 104.
Herefrom are calculated the illumination, i, plotted in Figs. 103
and 104 and recorded in Table IV for lv = 20 ft. ; p = 5, hence
lho = 100 ft., Fig. 103, and p = 10, hence lho = 200 ft., Fig. 104,
for equal light flux of 200 mean spherical candle power per lamp.
As seen, with the same light flux per lamp, the distribution
curve III of Fig. 100 gives the highest and the curve I the lowest
intensity at the minimum point midways between the lamps,
while inversely I gives the highest and III the lowest intensity
near the lamp; that is, I, the carbon arc with clear inner globe,
gives the least uniform, and III, the luminous arc, the most uni-
240
RADIATION, LIGHT, AND ILLUMINATION.
form, illumination, while the carbon arc with opal inner globe,
II, stands intermediate.
TABLE IV. — (Figs. 101 to 106.) STREET ILLUMINATION.
tan <h = x
tan 02 = p — x
tan <J»3 =
tan <f>4 =
X.
Equal light flux per lamp.
Equal illumination at minimum.
p = 10.
p= 5.
p = 10.
p= 5.
a.
6.
c.
a.
&.
c.
a.
b.
c.
a.
6.
c.
0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.5
3.0
3.5
4.0
5.0
15.8
22.8
46.8
74
74
68
54
40
32
26
20
12.7
8.2
6.3
4.9
4.2
23.7
25.7
34.7
44
46
42
37
32
27
23
19.5
14.6
11.3
9
8
6.7
31.7
32.7
33.5
33.5
33
32
30.5
29
26.5
24.5
22
18
15
13
11.5
10.2
20
27
51
78
78
72.5
59
45
37
32
29
25
29
31
40
50
52
48
43
38.5
35
32.5
30
29
41.5
42.5
43
43
43
42.5
41.5
40.5
39
37.5
36
34.5
38
54
111
176
176
162
128
95
76
62
48
30
20
15
12
10
35
38
52
66
69
63
55
48
40
34
29
22
17
13.5
12
10
31
32
32.7
32.7
32.3
31.4
30
28.4
26
24
22
18
15
13
11
10
8
11
20
31
31
29
24
18
15
13
11.6
10
10
11
14
17
18
17
15
13
12
11
10.4
10
12. 1~2
12.3
12.5
12.5
12.5
12.3
12.1
11.8
11.3
11
10.5
10
Ratio of minimum intensities.
Ratio of total light fluxes.
1
1.60
2.43
1
1.16
1.38
5.95
2.43
3.75
1.53
2.45
1.00
4.0(
1.3*
) 3.45 2.90
1 1.19 1.00
Ratio of maximum to min. ilium.
17.6
6.9
3.3
3.1
1.8 1.25
The ratio of maximum to minimum illumination is :
p = 10 p = 5
I. Carbon arc with clear globe: 17.6 3.1
II. Carbon arc with opal globe: 6.9 1.8
III. Luminous, or magnetite, arc : 3.3 1.25
LIGHT INTENSITY AND ILLUMINATION.
241
As seen, lower values of p, that is, either shorter distances
between the lamps, or greater elevation of the lamps above the
street surface, give a more uniform illumination, so that, for
p = 5, III gives only 25 per cent intensity variation, while, for
p = 10, I gives a very unsatisfactory illumination, alternating
darkness and blinding glare.
•0=2-
iO
100
140
160
r\
i
FIGS. 105, 106.
In Figs. 105 and 106 are plotted, and recorded in Table III, the
illuminations for equal minimum intensity midways between the
lamps, and for equal distances lho = 200 ft., between the lamps,
for
p = 5, or lv = 40 ft. height above the street level, Fig. 105.
p = 10, or 10 = 20 ft. height above the street level, Fig. 106.
To produce this minimum intensity of 0.1 candle feet, with
200 feet distance between the lamps, would require the following
mean spherical candle powers :
I. Carbon arc with clear globe: 1190
II. Carbon arc with opal globe: 750
III. Magnetite arc: 490
, or 4=40 ft.
800
690
580
242 RADIATION, LIGHT, AND ILLUMINATION.
It is interesting to note the great difference in the light flux,
required to produce the same minimum illumination, for the
three distribution curves.
The carbon arc gains in efficiency and in uniformity of illumi-
nation by increasing the elevation from 20 to 40 ft., while the
magnetite arc loses in efficiency —due to the greater distance
from the illuminated surfaces —but makes up for this by the
gain in uniformity of illumination.
C. ROOM ILLUMINATION BY INCANDESCENT
LAMPS.
106. Let Fig. 107 represent the intensity distribution of an
incandescent lamp with reflector, suitably designed for approxi-
mately uniform illumination in a horizontal plane below the
lamp. Such a distribution curve can, for instance, be produced
FIG. 107.
by a spiral filament F (Fig. 108) located eccentric in a spher-
ical globe G, of which the upper part is clear glass and covered
by a closely attached mirror reflector R, while the lower part
is frosted, as shown diagrammatically in Fig. 105.
With this arrangement, half of the light flux issues directly,
with approximately uniform intensity in the lower hemisphere,
from <j> = 0 to <j> = (f>l} and with gradually decreasing intensity
from $ = <£j to 0 at <£ = <j>2. The other half of the light flux is
LIGHT INTENSITY AND ILLUMINATION.
248
reflected from the mirror, and, due to the eccentric location of the
filament, the reflected rays are collected into an angle of about
45 deg. from the vertical, and cross each other, thereby producing
the intensity maximum
at 4> = 30 deg. The
intrinsic brilliancy is
sufficiently reduced,
and the distribution
curve smoothed out,
by the frosting of the
globe as far as not cov-
ered by the reflector.
The light in the upper
hemisphere beyond
</> = (j>2 then is only
that reflected by the
frosting.
The numerical val-
ues of intensity of Fig.
107 are recorded in
Table V.
The mean spherical
candle power of the
lamp is 12.93, or 163
lumens ; the mean can-
dle power in the lower
hemisphere is 20.20, or
127 lumens, and the mean candle power in the upper hemi-
sphere is 5.66, or 36 lumens.
Table V gives the distribution of illumination i in a horizontal
plane beneath and above the lamp, for different horizontal
distances lh and the vertical distance lv = 1, by equation (6),
and the horizontal illumination ih, by equation (7), as discussed
in A. These are plotted in Fig. 109, for the lower hemisphere
in the lower, for the upper hemisphere in the upper, curve.
Assuming now that a room of 24 ft. by 24 ft. and 10 ft. high
is to be illuminated by four such lamps, located 6 inches below
the ceiling in such a manner as to give as nearly as possible
uniform illumination in a plane 2.5 ft. above the floor (the height
of table, etc.).
FIG. 108.
244 RADIATION, LIGHT, AND ILLUMINATION.
TABLE V. — (Figs. 107 to 109.)
#.
7.
lh
lv
tan c£.
i =
I
COS2<£
**~
/
Ik
X = TV
i —
I
cosV
fc*-
/
cos3^
(Upper
hemisphere).
cos3 tf,
if.
i'h-
0
10
20
30
40
50
60
65
70
75
80
85
90
95
100
105
110
115
120
130
140
150
160
170
180
21.0
22.2
24.5
26.3
25.5
22.5
20.0
19.0
18.0
17.0
16.0
15.0
13.0
11.0
9.5
8.0
7.0
5.5
4.5
3.0
2.5
2.2
2.0
2.0
2.0
0
0.176
0.364
0.577
0.839
1.192
1.732
2.144
2.745
3.732
5.671
11.43
00
11.43
5.671
3.732
2.745
2.144
1.732
1.192
0.839
0.577
0.364
0.176
0
21.0
21.5
21.7
19.8
15.0
9.3
5.0
3.4
2.15
1.13
0.49
0.11
0
0.08
0.29
0.53
0.84
1.00
1.12
1.23
1.47
1.66
1.77
1.94
2.0
21.0
21.3
20.4
17.0
11.5
6.0
2.5
1.44
0.74
0.29
0.08
0.01
0
0.01
0.08
0.14
0.29
0.42
0.56
0.80
1.13
1.43
1.66
1.91
2.0
o
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.5
3.0
3.5
4.0
4.5
5.0
6.0
7.0
8.0
9.0
10.0
21.0
21.25
21.55
21.8
21.6
20.8
19.4
17.7
15.8
13.9
12.2
10.6
9.2
5.1
7.2
6.45
5.8
5.2
4.7
4.2
3.9
2.55
1.8
1.33
1.0
0.8
0.67
0.45
0.33
0.25
0.20
0.17
21.0
21.1
21.3
21.0
20.0
18.5
16.5
14.3
12.3
10.4
8.6
7.2
6.0
5.1
4.2
3.55
3.1
2.65
2.25
1.95
1.7
1.0
0.6
0.37
0.25
0.18
0.13
0.10
0.08
0.05
2.0
2.0
*i'.i
1.5
1.35
1.0
1.2
0.68
Y.08
0.9
0.77
0.63
0.5
0.43
0.38
0.28
0.20
0.17
0.14
0.12
'b'.48
0.35
0.27
0.20
0.13
0.10
0.08
0.06
As the illumination in the space between the lamps is due
to several lamps and thus is higher than that at the same horizon-
tal distance outside of a lamp, for approximate uniformity
of illumination, the distance between the lamps must be con-
siderably greater than twice their distance from the side walls
LIGHT INTENSITY AND ILLUMINATION. 245
0*6
08
II
246
RADIATION, LIGHT, AND ILLUMINATION.
of the room. Locating thus the lamps, as shown diagrammati-
cally in Fig. 110, at 5 ft. from the side walls and 14 ft. from each
other, the (total) illumination in the lines A, B, C, D in the
test plane 2.5 ft. above the floor is calculated. As this plane is
7 ft. beneath the lamps, first the illumination curve in a plane
7 ft. beneath the lamp is derived from that in Fig. 109, by
dividing the ordinates by 72 = 49, and multiplying the abscissas
by 7. It is given in Fig. 111.
FIG. 111.
The illumination, i, at any point, P, then is derived by adding
the illumination ia, ib, ic, id of the four lamps a, 6, c, d, taken
from curve in Fig. Ill for the horizontal distances of point P
from the lamps : lhg, lhb, lhc, lhd. These component illuminations
are plotted in Figs. 112 to 115; as A , Ab, Ac, Ad in Fig. 112; as
Ba, Bb in Fig. 113, etc., and their numerical values, in thousandths
of candle feet, recorded in Table VI. In Fig. 116 are shown
the four curves of the resultant direct illumination, superim-
posed upon each other.
107. To this direct illumination is to be added the diffused
illumination G resulting from reflection by ceiling and walls.
Let: at = 0.75 = albedo of ceiling;
a2 = 0.4 = albedo of walls;
(19)
while the floor may be assumed as giving no appreciable reflec-
tion: a = 0. The diffused light, then, may be approximated
as follows:
The ceiling receives as direct light the light issuing in the upper
hemisphere, or 36 lumens per lamp, thus a total of
Lx = 4 X 36 = 144 lumens, (20)
LIGHT INTENSITY AND ILLUMINATION.
TABLE VI. — (Figs. 110 to 116.)
247
X.
Aa.
Ab.
A.
Ba
and
Bd-
B.
ca.
cb.
C.
Da-
Db
and
Dc.
D.
0
353
71
746
180
690
244
43
600
245
43
600
1
406
74
813
200
738
276
44
645
317
49
691
2
438
76
852
218
782
306
44
681
395
55
785
3
442
78
866
234
822
332
45
714
441
62
845
4
438
80
875
244
852
348
45
737
440
70
866
5
429
80
880
247
870
353
45
746
429
79
880
6
438
80
903
244
882
348
45
754
440
90
919
7
442
78
922
234
880
332
45
750
441
101
949
8
438
76
936
218
866
306
44
737
395
114
939
9
406
74
927
200
850
276
44
723
317
125
896
10
353
71
898
180
838
244
43
710
245
135
859
11
298
67
875
162
830
209
42
696
184
143
835
12
247
63
870
144
825
180
41
690
144
144
825
13
flOO
60
129
156
39
115
143
14
167
57
114
136
37
94
135
15
143
54
102
118
35
79
125
16
121
51
90
103
33
66
114
17
104
48
81
90
31
56
101
18
90
45
72
80
30
49
90
19
80
41
63
72
30
42
79
20
70
38
57
64
30
36
70
21
61
35
52
58
29
33
62
22
55
33
48
52
29
30
55
23
52
31
44
47
28
26
49
24
45
2P
40
43
28
23
43
and also receives some reflected light from the walls. Thus,
if ^ = total light flux received by the ceiling, and 3>2 = total
light flux received by the walls, the light flux received by the
ceiling is
^ = L, + b2a23>2, (21)
where b2 is that fraction of the light flux issuing from the walls,
which is received by the ceiling.
And the light reflected from the ceiling thus is :
$/= afr = a, (L, + b2a2$>2). (22)
The walls receive as direct light the light issuing from the
lamps in the lower hemisphere, between the horizontal, <f> = 90
248
RADIATION, LIGHT, AND ILLUMINATION.
deg., and the direction, <£ = a) (Fig. 110), from the lamp to the
lower edge of the walls. This angle co varies, and averages
30 deg. for that half of the circumference, PQR (Fig. 110), at
which the walls are nearest, and 60 deg. for that half, RSTUP,
for which the walls are farthest, from the lamp. Hence the
1.0
0.8
0.6
0.4
0.2
Act
Ac
12 10
0.8
B
0.6
0.4
G
0,2
BaScd
BbStc
6 *c
B
B
G
Bfc&c
Bakd
X
x- —
** -^
-^
-*
^»
-•>s
X
/
\
-*-
^^
^^**
>J
^
_ ~~
_ -
—. •—
, — •
- —
- -,
~- ..
•• —
4 8 12 18 20 2*
FIGS. 112, 113.
light flux received by the walls as directed light, from each lamp,
is
- I I sin $ d$ + - T / sin $ d$ = 83 lumens; (23)
Zt/30° ^^60°
or, a total of L2 = 4 X 83 = 332 lumens. (24)
LIGHT INTENSITY AND ILLUMINATION.
249
In addition hereto, the walls receive some of the light flux
reflected by the ceiling. The total light received by the walls
thus is :
$2 = L2 + bpfr, (25)
where bl is that fraction of the light flux issuing from the ceiling,
which is received by the walls.
1.0
0.8
0.6 C
G
0.2 Ca
Cb
Cd
0 Cc
1.0
Cb
12 16 20
0.8
0.8 D
O.i
0.2
Dbbd
0 DC
Da
FIGS. 114, 115.
And the light reflected from the walls thus is :
*,' - a^2 = a2 (L2 + 6^*,). (26)
It thus remains to calculate the numerical values of bl and by
Of the light reflected by the ceiling as secondary generator,
/, a part is obstructed by the floor, a part received by the walls.
250
RADIATION, LIGHT, AND ILLUMINATION.
The floor is a square plane, of the same size, 24 by 24 ft., as the
radiator, that is, the ceiling, and at the distance 10. The light
intercepted by the floor can thus approximately be calculated
as discussed in Lecture X, II, 1, Fig. 82, for circular radiator
and circular shades, by replacing the quadratic shade and radia-
tor by circular shades of the same area, r2n = 242, and r =
13.5, at the same distance I = 10, hence of the ratio : - = 0.74.
Calculated as discussed in Lecture X, II, 1, the floor receives
55 per cent and the walls 45 per cent of the light reflected by the
ceiling.
Assuming, approximately, that the walls receive the same
percentage of the light reflected from the ceiling, as the ceiling
receives of the light reflected from the walls, or
&2 - &!, (27)
equations (21) and (25) become:
^ = L,+ \a2$>2, (28)
<f>2 = L2+ 6^^; (29)
hence,
_L2+
2 1 +
(30)
and the light reflected from the ceiling is
$/ = a^ = «A — — * 2 2;
the light reflected from the walls is
<L ' dS ^2~^~ biaiLl
(30)
hence, substituting the numerical values :
$/ = 146 lumens and $/ = 144 lumens "
are the values of light reflected from the ceiling and from the
walls respectively.
Of that from the ceiling, the floor receives (1 - 6J = 0.55,
and of that from the walls, the floor receives ll = 0.45; hence,
LIGHT INTENSITY AND ILLUMINATION.
251
the diffused light on the floor plane, and thus also, sufficiently
approximate, on the test plane 2.5 ft. above the floor, is
*.= (! -&,)*,'+&,*,'
= 145 lumens,
and as this plane contains At = 576 sq. ft., the flux of diffused
light per square foot in the test plane, or the diffuse illumination,
is L = -r = 0.250 foot-candle.
r.oo
500
400
300
200
100
/
£
/
FIG. 116.
108. Adding this diffuse illumination, shown as G, to the
directed illumination, gives the total illumination, i, shown
as A, B, C, Dm Figs. 112 to 115, and recorded in Table VI.
From these curves are taken the values of the distance,
Table VII, at which the total illumination passes 0.600; 0.650;
0.700, etc., foot-candle, and plotted in Fig. 117. The points of
equal illumination, then, are connected by curves, and thus
give what may be called equi-luminous curves, or equi-potential
curves of illumination.
These equi-luminous curves are plotted for every 0.05 foot-
candle, except that the curves 0.875 and 0.925 are added in
252 RADIATION, LIGHT, AND ILLUMINATION.
dotted lines. As seen, the illumination is a minimum of 0.600
in the corners of the room and a maximum of 0.950 at a point
between the lamps and the center of the room, and is between
0.800 and 0.950 everywhere except close to the edges of the
room.
FIG. 117
TABLE VII.— (Fig. 117.) EQUI-POTENTIAL CURVES.
t.
A.
B.
C.
D.
600
o
o
625
55
28
650
1 15 rC440)l
56
675
1 80 L12 OOJ
82
700
.20
2 57 10 70
1 09
725
70
3 45 8 85
1 37
750
775
800
825
.05
.37
.77
1.21 f (620)1
1.24
1.88
2.45 r(576)l
3.08 Ll2 OOJ
5.50 7.00
6.30
(505)
1.61
1.88
2.18 r(576)l
2 50 L12.00J
850
1.90 Ll2.00J
3.88 9.00
3 10 10.35
875
4.00 11.00
5.30 7.47
4 70 9.50
900
5.90 9.90
6.40
5.53 8.90
925
7.15 9.10
(634)
6.13 8.32
950
8.20
7 20
(686^
Cjc\f\\
LIGHT INTENSITY AND ILLUMINATION. 253
The direct light, which reaches the test plane, 2.5 ft. above
the floor, as directed light from the lamps, issues within the angle
from the vertical, <£ = 0, up to from <£ = 40 deg. to 0 = 70
deg., and is 75 lumens per lamp; or, a total of directed light in
the test plane of 4 X 75 = 300 lumens. The diffused light in
the test plane is 576 X 0.25 = 144 lumens, and the total light
in the test plane thus is 444 lumens; while the total light
issuing from the four lamps is 4 X 163 = 652 lumens, giving an
444
efficiency of illumination of ; - = 0.68; or, 68 per cent: the
652
444
average horizontal illumination in the test plane is ihm = — - =
o7o
770; while the average total illumination, from Fig. 117, is
about im = 870. The difference is due to the varying direction
in which the directed light traverses the test plane.
Measurement of the illumination of a room by illuminometer,
to give correct values, thus must take in consideration the
different directions in which the light traverses every point;
by measuring the light flux intercepted by a horizontal sur-
face, the result represents only the horizontal illumination,
and not the total illumination at the point measured, and
therefore frequently does not represent the illuminating value
of the light.
D. HORIZONTAL TABLE ILLUMINATION BY INCAN-
DESCENT LAMPS.
109. Assuming a table, of 5 ft. by 13 ft., to be illuminated
so as to give as nearly as possible uniform horizontal illumina-
tion ih. With a light source of the distribution curve, Fig. 107,
but of four times the intensity, and using two such lamps, they
would be located vertically above the table, at a distance from
each other which would be chosen so that, midways between
the lamps, the illumination is approximately the same as verti-
cally beneath the lamps.
In the same manner as discussed in C, the illumination is
calculated in characteristic lines, indicated as A, B, C in Fig.
118, using, however, the curve ih of Fig. 109.
About the most uniform horizontal illumination then is given
by locating the lamps 5 ft. above the table, 8 ft. from each
254 RADIATION, LIGHT, AND ILLUMINATION.
other and 2.5 ft. from the edge of the table, as shown in Fig. 118.
The illuminations in the lines A, B, and C, and their components
are plotted in Figs. 119, 120, 121, and recorded in Table VII.
A —
1
(
f ' T
(f
k---J
B. ^
fr-2.5— »
,
^ 4 ^
v _
2J5
"^
2|5
i
6
FIG. 118.
TABLE VIII.— (Figs. 118 to 121.) HORIZONTAL ILLUMI-
NATION OF TABLE.
X.
Aa.
Ab.
A.
Ba.
Bb.
B.
Ca'b.
C.
-2.5
-2.0
— 1.5
2.96
3.20
3.36
0.24
0.27
0.32
3.20
3.47
3.68
2.96
3.20
3.36
0.38
0.46
0.48
3.34
3.66
3.84
1.55
1.66
1.79
3.10
3.32
3.58
— 1.0
— 0.5
0
3.41
3.37
3.36
0.37
0.43
0.50
3.78
3.80
3.86
3.41
3.37
3.36
0.48
0.50
0.50
3.89
3.87
3.86
1.89
1.96
1.97
3.78
3.92
3.94
+ 0.5
1.0
1.5
3.37
3.41
3.36
0.57
0.67
0.81
3.94
4.08
4.17
3.37
3.41
3.36
0.50
0.48
0.48
3.87
3.89
3.84
1.96
1.89
1.79
3.92
3.78
3.58
2.0
2.5
3.0
3.2
2.96
2.63
0.96
1.15
1.37
4.16
4.11
4.00
3.20
2.96
0.46
0.38
3.66
3.34
1.66
1.55
3.32
3.10
3.5
2.28
1.66
3 94
+ 4.0
1.96
1.96
3.92
LIGHT INTENSITY AND ILLUMINATION.
255
From the curves as given in Figs. 119 to 121 may then be
plotted the equi-luminous curves at the table surface, as done
in Fig. 117 of the preceding paragraph. In this case, which
represents concentrated illumination, diffusion is not considered,
but the light is all directed light.
A
141
FIG. 119.
4.0
3.0
2.0
1.0
4,0 4.0
3.0 3.0
2.0 2.0
1.0
/"
N,
/
\
^
^
"""--
\
i
FIG. 120.
FIG. 121.
LECTURE XII.
ILLUMINATION AND ILLUMINATING ENGINEERING.
110. Artificial light is used for the purpose of seeing and
distinguishing objects clearly and comfortably when the day-
light fails. The problem of artificial lighting thus comprises con-
sideration of the source of light or the illuminant; the flux of
light issuing from it; the distribution of the light flux in space,
that is, the light flux density in space and more particularly at
the illuminated objects; the illumination, that is, the light flux
density reflected from the illuminated objects, and the effect
produced thereby on the human eye. In the latter, we have left
the field of physics and entered the realm of physiology, which is
not as amenable to exact experimental determination, and where
our knowledge thus is far more limited than in physical science.
This then constitutes one of the main difficulties of the art of
illuminating engineering: that it embraces the field of two dif-
ferent sciences — physics and physiology.
The light flux entering the eye is varied in its physical quantity
by the reaction of the eye on light flux density in contracting
or expanding the pupil. The effect of the light flux which enters
the eye is varied by the fatigue, which depends on intensity and
also on color. Distinction is due to differences in the light flux
density from the illuminated objects, that is, differences of
illumination, which may be differences in quality, that is, in
color, or differences in intensity, that is, in brightness, and as
such includes the effect of shadows as causing differences in
intensity at the edge of objects.
The physical quantities with which we have to deal in illumi-
nating engineering thus are :
The intensity of the light source or the illuminant, and its
brilliancy, that is, the flux density at the surface of the
illuminant;
The flux of light, that is, the total visible radiation issuing
from the illuminant;
256
ILLUMINATION AND ILLUMINATING ENGINEERING. 257
The light flux density, that is, the distribution of the light flux
in space, and
The illumination, that is, the light flux density issuing from
the illuminated objects.
The intensity of a light source is measured in candles. The unit
of light intensity, or the candle, is a quantity not directly related
to the absolute system of units, but reproduced from specifica-
tions or by comparison with maintained standards, and for
white light is probably between 0.04 and 0.02 watt. Intensity
has a meaning only for a point source of light; that is, an illumi-
nant in which the flux of light issues from a point or such a small
area that, at the distance considered, it can be considered as a
point. " Intensity of light " thus is a physical quantity of the
same nature as " intensity of magnet pole," which latter also
presupposes that the total magnetic flux issues from a point,
and thus is applicable only when dealing with such distances
from the source of the light flux or magnetic flux, that the flux
can be assumed as issuing from a point. Frequently the inten-
sity of a light source is different in different directions, and then
either the distribution curve of the light intensity is required for
characterizing the illuminant, or the average of the intensities in
all directions in space is used, and is called the "mean spherical
intensity."
The unit of light intensity, or the candle, is the intensity
which produces unit flux density at unit distance from the light
source, and thus produces a total flux of light equal to 4 n
units (the surface of the sphere at unit distance from the light
source). The unit of light flux is called the lumen, and one
candle of light intensity thus produces 4 n lumens of light flux
(just as a magnet pole of unit intensity produces 4 x lines of
magnetic force).
The light flux is the essential quantity which characterizes
the usefulness of an illuminant, and it is the raw material from
which all illuminating engineering starts. Any source of light
can be measured in units of light flux or lumens — the diffused
daylight entering the windows of a room, or the visible radia-
tion of the mercury lamp or a Moore tube as well as that of a
point source — by adding all the flux densities intercepted by
any surface enclosing the source of light.
In a point source of light, the intensity, in candles, is the total
258 RADIATION, LIGHT, AND ILLUMINATION.
flux of light, in lumens, divided by 4 x. In any illuminant
which is not a point source, we cannot speak of an intensity,
except at such distances at which the source of light can be
assumed as a point; and in interior illumination this is rarely
the case. Since, however, the candle power, as measure of the
intensity of light, has become the most familiar quantity in
characterizing illuminants, very commonly even sources of light
which are not point sources — as a Moore tube or the diffused
daylight — are expressed in " equivalent candle power" and when
thus speaking of the candle power of a mercury lamp, or of the
diffused daylight from the windows, we mean the candle power
of a point source of light, which would give the same total flux
of light as the mercury lamp, or the daylight from the windows,
etc. The " equivalent candle power," or frequently merely called
" mean spherical candle power/' thus is the total light flux divided
by 4 TT, hence in reality is not a unit of intensity, but a unit of
light flux.
This explains the apparent contradiction between the claims
that sources of light, as the mercury lamp or the Moore tube, can-
not be expressed in candle powers, while at the same time their
specific consumptions are given in candle power per watt : mean-
ing equivalent candle power, which refers to the total flux of
light, and thus is a definite and measurable physical quantity.
While it is not probable that the custom of rating illuminants
in candles, regardless of their shape, will quickly disappear, and
no objection exists against it, provided that it is understood to
mean the equivalent candle power, it is preferable to use the cor-
rect unit of light flux, and express the output of a source of light
in lumens, adding where necessary the equivalent candle power
in parenthesis. Obviously, the use of the candle power in any
particular direction — horizontal, or terminal, or maximum can-
dle power — has a meaning only in characterizing the distribution
of the light flux, as applicable for a particular purpose, as street
lighting, but, when used for rating the illuminant by its light flux
output, is an intentional or unintentional deception. Incandes-
cent lamps have been rated, and to some extent still are, in hori-
zontal candle power, but in this case the horizontal candle power
has ceased to mean the actual horizontal candle power, but is
the horizontal candle power which with a certain standard dis-
tribution of light flux would correspond to the light flux of the
ILLUMINATION AND ILLUMINATING ENGINEERING. 259
lamp, and thus also is merely a practical measure of the light
flux, retained by convenience : one horizontal candle power rep-
resents 0.78 mean spherical or equivalent candle power of the
standard distribution curve, and thus 4 TT X 0.78 lumen.
In general, intensity, or candle power, thus is an angular
measure, useful in characterizing the distribution of the light
flux, but not the total light flux.
111. Light- flux density is the light flux per unit area traversed
by it, thus is measured in lumens per square meter (or square
foot), just as the magnetic density is measured in lines of mag-
netic force per square centimeter. In illumination, as unit of
length, usually the meter is employed, and not the centimeter, as
in the absolute system of units, and 102 thus is the reduction
factor to absolute units. Frequently also the foot is used as
practical unit of length.
For a point source of light the light flux density is the inten-
sity of the light source, in candles (in the direction towards the
point of observation, if the distribution is not uniform in all
directions), divided by the square of the distance, in meters,
or feet, and the light flux density thus is frequently expressed
in meter-candles, or foot-candles. Thus at 10 feet distance from
a 16 candle power lamp, the light flux density is 0.16 foot-candle,
or 0.16 lumen per square foot. Very commonly, therefore,
the light flux density produced by sources of light which are
not points, is also expressed in meter-candles or foot-candles —
which numerically is the same value, that is, the same quantity,
as lumens per square meter or square foot, but physically
would refer to the equivalent candle power of the light source.
Illumination is the light flux density reflected from the illu-
minated object, and as flux density thus is measured also in
lumens per square meter or square foot, or in meter-candles or
foot-candles.
Brilliancy is the light flux density at the surface of the illumi-
nant, and as flux density thus could also be measured in lumens
per square meter or square foot, but, as this would usually give
enormous values, brilliancy of the light source generally is meas-
ured in lumens per square centimeter, or per square millimeter.
It is a quantity which is of high importance mainly in its physio-
logical effect.
Light intensity, brilliancy and light flux thus are character-
260 RADIATION, LIGHT, AND ILLUMINATION.
istics of the illuminant, while flux density is a function of the
space traversed by the light flux, but not of the source of light :
with the same source of light, in the space from the surface of
the illuminant to infinite distance, all light flux densities exist
between the maximum at the surface of the illuminant (its
brilliancy) and zero. Brilliancy thus is the maximum of the
light-flux density. While intensity and brilliancy depend upon
the shape of the illuminant, light flux is independent thereof.
Illumination is a quantity which depends not only on the source
of light, that is, light flux and flux density, but also on the illumi-
nated objects and their nature, and thus is the light flux density
as modified by the illuminated objects. Very commonly, how-
ever, the term " illumination " is used to denote " light flux
density," irrespective of the illuminated objects.
112. The light flux thus is the raw material with which
illuminating engineering starts, and the first problem then is
to distribute the light flux through space so as to give at all
points the light flux density required for satisfactory illumi-
nation.
Some problems, as the lighting of a meeting place, school-
room, etc., require a uniform or general, and fairly high intensity
of illumination, while in street lighting a uniform but fairly low
intensity of illumination is desirable. In other cases, mainly a
local or concentrated illumination is needed. Usually, however,
a combination of a local or concentrated illumination, of fairly
high intensity, with a general illumination of lower intensity,
is required: the former at those places where we desire to
distinguish details, as where work is being done, at the reading-
table, work bench, dining-table etc., while the general illumina-
tion is merely for orientation in the space, and thus may be of
lower intensity, and for reasons of economy, and also physio-
logical reasons, should be of lower intensity.
We thus have to distinguish between local or concentrated,
and general or uniform, illumination, and a combination of
both, and have to distribute the light flux in accordance there-
with, that is, produce a high flux density at the points or areas
requiring high concentrated illumination, a low and uniform
flux density throughout the remaining space.
This can be done by choosing a light source of the proper
distribution curve, as, for instance, in street illumination a lamp
ILLUMINATION AND ILLUMINATING ENGINEERING. 261
giving most of the light flux between the horizontal and 20 deg.
below the horizontal; in many cases of indoor illumination
a light source giving most of the light between the vertical
and an angle of from 30 to 60 deg. from the vertical — depending
on the diameter of the area of concentrated illumination and
the height of the illuminant above it. It can also be done by
modifying or directing the light flux of the illuminant by reflec-
tion or diffraction and diffusion, either from walls and ceilings
of the illuminated area, or by attachments to the illuminant,
as reflectors, diffusing globes, diffracting shades, etc. Further-
more, the required flux distribution can be secured by the use
of a number of illuminants, and with a larger area this usually
is necessary. Frequently the desired flux distribution is pro-
duced by using an illuminant giving more light flux than neces-
sary, and destroying the excess of flux in those directions where
it is not wanted, by absorption. Obviously this arrangement
is uneconomical and thus bad illuminating engineering; the
desired flux distribution should be secured economically, that
is, without unnecessary waste of light flux by absorption, and
this usually can be done by a combination of a number of light
sources of suitable distribution curves. The most economical
method of securing the desired distribution curve obviously is
to choose a light source coming as near to it as possible, and
then modifying it by reflection or diffraction.
113. Thus far, the problem is one of physics, and the result,
that is, the objective illumination, can be measured by photometer
or luminometer, and thus checked. The duty of the illuminat-
ing engineer, however, does not end here, but with the same
objective illumination, that is, the same distribution of light
flux throughout the entire illuminated area, as measured by
photometer, the illumination may be very satisfactory, or it
may be entirely unsatisfactory, depending on whether the physio-
logical requirements are satisfied or are violated ; and very often
we find illuminations which seem entirely unsatisfactory, tiring,
or uncomfortable, but when judged by the density and the
distribution of the light flux, should be satisfactory. Even
numerous commercial illuminants, designed to give suitable
distribution curves, fail to do justice to their light flux and
its distribution, by violating fundamental physiological require-
ments.
262 RADIATION, LIGHT, AND ILLUMINATION.
The physiological problems of illumination, that is, the effects
entering between the objective distribution of light flux in space,
and the subjective effects produced on the human eye, thus are
the most important with which the illuminating engineer has to
deal, and the first feature which must be recognized is that the
objective illumination, as measured by the photometer, is no
criterion of the subjective illumination, that is, the physiological
effect produced by it, as regard to clearness, comfort and satis-
faction, and it is the subjective illumination by which the success
of an illuminating engineering problem is judged.
The most important physiological effects are :
(a) The contraction of the pupil. The pupil of the eye auto-
matically reacts, by contraction, on high brilliancy at or near
the sensitive spot, that is, the point of the retina, on which we
focus the image of the object at which we look, and to a some-
what lesser extent on high brilliancy anywhere else in the field
of vision. If, therefore, points or areas of high brilliancy are
in the field of vision, especially if near to objects at which we
look, the pupil contracts the more the higher the brilliancy,
and thereby reduces the amount of light flux which enters the
eye, that is, produces the same result as if the objective
illumination had been correspondingly reduced, intensified by
the uncomfortable effect of seeing high brilliancy. The exist-
ence of points of high brilliancy in the field of vision thus results
in a great waste of light flux, and additional discomfort, and, for
satisfactory illumination, points of high brilliancy thus must
be kept out of the field of vision. Light sources of high brilliancy
must be arranged so that they cannot directly be seen, but the
illumination accomplished by the light reflected from ceilings,
etc., or from reflectors attached to the illuminant: indirect light-
ing; or at least the light sources should be located where we
are rarely liable to look at them, that is, with moderate-sized
rooms, at or near the ceilings. Or light sources of moderate
intrinsic brilliancy should be used, as the Moore tube, the
mercury lamp, the Welsbach mantel. Or, with illuminants of
high brilliancy, as the electric arc, the incandescent lamp
(especially the tungsten filament), etc., the brilliancy of the
illuminant must be reduced by enclosing it with a diffusing or
diffracting globe or shade, as an opal or frosted or
holophane globe, etc.
ILLUMINATION AND ILLUMINATING ENGINEERING. 263
No illumination, however, can be satisfactory in which the
eye at any time can be exposed to the direct rays from a tungsten
filament or an arc. While the methods of removing the high
brilliancy of the illuminant usually involve a considerable loss of
light flux, by absorption at the refracting surface, in the frosted
or opal globe, etc., and the objective illumination thus is de-
creased, if the methods of reducing the brilliancy are anywhere
reasonably arranged, the light flux entering the eye, and thus
the subjective illumination, is increased, and often very greatly.
Thus while frosting an incandescent lamp decreases its light
flux by about 15 per cent, in spite thereof usually more light
flux enters the eye from the frosted lamp than from a clear glass
lamp at the same distance.
It is, therefore, inefficient to use illuminants of high brilliancy
in the field of vision, and in addition makes the illumination
uncomfortable and thereby unsatisfactory. Physiologically the
brilliancy of the light source thus is one of the most important
quantities.
114. (6) Fatigue. When exposed to fairly high light flux den-
sity, that is, high illumination, the nerves of the eye decrease
in sensitivity, by fatigue, and inversely, in lower illumination
or in darkness, increase in sensitivity. This reaction, or adjust-
ment of the sensitivity of the nerves of vision to different intensi-
ties of illumination, enables us to see equally well in illuminations
varying in intensity by more than 10,000 to 1 (as daylight and
artificial light). Thus, when entering a well-illuminated room
from the darkness, it first appears glaring, until gradually
the impression fades down to normal. Inversely, coming from
a well-lighted room into a space of much lower illumination, it
first appears practically dark, until gradually the eye adjusts
itself, that is, the nerves of vision increase in sensitivity by their
rest, and then we again see fairly well.
Fatigue and contraction of the pupil thus are similar in their
action, in that they reduce the physiological effect for high
intensities. The contraction of the pupil, however, is almost
instantaneous, and is a protective action against excessive bril-
liancies in the field of vision, while the fatigue is a gradual
adjustment to the average intensity of illumination, within the
operating range of the human eye.
By exposure for a considerable period to the fairly high illumi-
264 RADIATION, LIGHT, AND ILLUMINATION.
nation required when working by artificial light, the sensitivity
of the eye decreases, the illumination appears less bright, and
thus a higher illumination is required than would be sufficient
in the absence of fatigue, and the continuous use and absence
of rest cause the sensation of strain, that is, irritation or an
uncomfortable feeling, as especially noticeable when working
or reading for a considerable length of time in rooms having a
high uniform intensity of illumination, as meeting-rooms, some
libraries, etc. If, however, the eye can rest even momentarily,
by a change to lower intensity of illumination, fatigue is decreased,
never becomes as complete and uncomfortable, and the concen-
trated illumination of the working-table appears brighter than
it would without the possibility of rest.
A room having a uniform intensity of illumination thus appears
glaring and uncomfortable, and for satisfactory illumination
it is necessary not only to provide a sufficiently high intensity
at the place where needed, but it is just as necessary to keep
the intensity of illumination as low as permissible, wherever
it is not needed, so as to afford to the eye rest from the fatigue.
In some cases, as meeting-halls, schoolrooms, this may not be
possible, but a uniform high intensity required, to be able to
work or read anywhere in the room. Where, however, it is not
necessary, it is not merely uneconomical to provide a uniform
high intensity of illumination, but it is an illuminating engineer-
ing defect, and a high intensity should be provided, as concen-
trated illumination, only at those places where required, as
at the reading-tables of the library, but the general illumination
should be of lower intensity. While we rarely realize the cause,
we feel the superiority of the combination of high concentrated
and lower general illumination, by speaking of such illumination
as home-like, restful, etc. Especially in places where considerable
work has to be done by artificial illumination, as in libraries,
factories, etc., to get satisfactory results, it is important to
consider this effect of fatigue, and to properly combine a moder-
ately low general illumination with a local higher intensity of
illumination at the places of work. The latter can usually be
given by a light source having a downward distribution, located
sufficiently high above the place of work. The average standing
or reading lamp, however, generally is not sufficiently high to
accomplish the result. Obviously, in such local illumination,
ILLUMINATION AND ILLUMINATING ENGINEERING. 265
the brilliancy of the illumination must be kept low, as discussed
above.
Of considerable importance regarding fatigue is the quality,
that is, the color, of the light : fatigue at high intensities occurs
far more with yellow and orange rays than with white light,
and very little with green and bluish-green light. Thus, in arti-
ficial illumination, in which practically always the yellow and
orange rays greatly preponderate, the question of fatigue is far
more important than with the bluish-white diffused daylight,
and the irritating effects of fatigue thus are mostly felt with
artificial illumination.
115. (c) Differences. Objects are seen and distinguished by
differences in quality, that is, color, and in intensity, that is,
brightness, of the light reflected by them. If there were no
differences in color or in intensity throughout the field of vision,
we would see light but would not distinguish objects. Therefore,
in good illumination, the differences in color and in intensity
should be sufficiently high to see clearly by them, but still limited
so as not to preponderate to such extent as to distract the atten-
tion from smaller differences. The differences in intensity,
to give distinction, should be high, but at the same time are
limited by the phenomena of fatigue and of the contraction
of the pupil: the minimum intensity must still be sufficiently
high to see clearly, and the maximum intensity not so high as
to cause fatigue and contraction of the pupil, much beyond
that corresponding to the average intensity, otherwise the vision
becomes indistinct and unsatisfactory, and uncomfortable by
too much contrast; that is, the intensity differences must give
a sufficient, but not an excessive, contrast, if the illumination is
to be satisfactory.
Differences in quality, that is, in color, are to a limited extent
only under the control of the illuminating engineer. In some
cases the illuminating engineer can control or advise regarding
the color of objects, as the walls, ceilings, etc. In most cases,
however, the absolute color of the illuminated objects is not within
the control of the illuminating engineer: for instance, in street
lighting, the color of the street surface, its surroundings, as
vegetation, houses, etc., are fixed and cannot be changed for
effects of illumination. So also in most cases of indoor illumina-
tion. To some extent, however, the subjective color can be con-
266 RADIATION, LIGHT, AND ILLUMINATION.
trolled by the choice of the proper shade of light, and thereby
slight color differences increased and made more distinct, or
decreased and thus obliterated. For instance, the color resulting
from age and dirt is usually the color of carbon and of iron,
yellowish brown or reddish brown, that is, colors at the long
wave end of the spectrum. Spots and blemishes due to dirt
or age, thus are made more distinct by using an illuminant defi-
cient in the long waves of light, as the mercury lamp, while in-
versely they are decreased by using a reddish-yellow illuminant,
as the incandescent lamp or the candle. Thus the white arc
lamp and still more so the bluish-green mercury lamp shows
blemishes and slight color differences of age and dirt harsh and
exaggerated, while the yellow light softens them and makes
them disappear; and while, for a ballroom, the yellow light
is thus preferred, and the mercury arc or even the ordinary
white carbon arc would give a harsh and disagreeable effect,
inversely the yellow light would be unsuitable where such slight
differences should be distinguished. It is therefore essential
for the illuminating engineer to choose as far as it is feasible the
proper color of light, and an otherwise good illumination may be
spoiled by using too white or too yellow a light.
The main distinction of objects, however, is due to differences
in intensity or brightness, and, for producing these, the shadows
are of foremost assistance, and indeed the differences of inten-
sity, by which we see objects, are to a large extent those due
shadows. The study of the shadow thus is one of the most
important subjects of illuminating engineering. If we have no
shadows, but a perfectly diffused illumination, even if the
intensity of illumination is sufficient, the illumination is unsatis-
factory, as we lose the assistance of the shadows in distinguishing
objects, and therefore find seeing more difficult, the illumination
restless and uncomfortable.
The use of shadows for illumination requires that we must
have directed light, that is, light coming from one or a number
of sources, and thus causing shadows, and not merely diffused
illumination, that is, light coming from all directions and thus
causing no shadows. While, however, in general perfectly dif-
fused illumination is unsatisfactory, an illumination having only
directed light is also unsatisfactory. If the light is all directed,
as from a single arc, the shadows are absolutely black, we can-
ILLUMINATION AND ILLUMINATING ENGINEERING. 267
not see anything in them, and, in attempting to see the objects
in the shadows, the illumination becomes tiring to the eyes,
irritating and restless.
For satisfactory illumination, it therefore is necessary to
have sufficient directed light to mark the edge of the objects
by their shadow, and thereby improve distinction, but at the
same time sufficient diffused light to see clearly in the shad-
ows; that is, a proper proportion of directed and diffused light is
necessary.
In cases in which all the objects assume practically the same
color, as in flour mills or foundries, a diffused illumination without
shadows would make the illumination so bad as to be practically
useless. In other cases, as a drafting-room, where all the objects
requiring distinction are in one plane, as the drafting board, and
the distinction is exclusively by differences of color and intensity,
but not by shadows, a perfectly diffused illumination is required,
and shadows would be objectionable and misleading, and this
is one of the cases where directed light is objectionable.
While with a single light source all the light issuing from it
is directed light, by using a number of illuminants, the overlap
of their light fluxes causes more or less light to reach objects
from all directions, and thereby gives the effect of diffused light,
except at those places where the shadows cast by the different
light sources coincide, and by proper positions of sufficient
numbers of light sources this can be avoided. The use of a
number of light sources thus offers a means of increasing the
proportion of diffused to directed light.
116. It is not sufficient, however, to have merely a combination
of diffused and directed light in the proper proportion, but the
direction of the latter also is of importance. In some simple
cases this is obvious, as, in writing, the directed light should
be from in front on the left side above the table, so as not to
cast the shadow on the work. The purpose of the shadow in
illumination is to mark the edge of the object, and its height
by the length of the shadow. The shadow, therefore, should
not extend too far from the object to which it is related, other-
wise it loses its close relation to it and becomes misleading and
thereby interferes with good illumination. Thus the directed
light should come from above, that is, in a direction making a
considerable angle with the horizontal, so as to limit the length
268 RADIATION, LIGHT, AND ILLUMINATION.
of the shadow without, however, being vertical, as the latter
would largely obliterate shadows. Perhaps an angle of 45 to
60 degrees with the horizontal would be most satisfactory.
The practically horizontal shadows cast in the usual form
of street lighting therefore are not satisfactory for best illumi-
nation.
The number of shadows is of less importance. While in nature
objects have one shadow only, cast by the sun, indoors we are
familiar with seeing several shadows due to the diffused day-
light from several windows. Of high importance, however, is
the shape of the illuminant, in so far as it determines the outer
edge of the shadow. The purpose of the shadow is to give an
intensity difference at the edge of the object, and thereby make
it easier to see the object. The shadow, however, has another
edge, its outer end, and that we should not see, as no object
ends there, or at least it must be such that it cannot be mistaken
for the edge of an object. The problem thus is not merely to
provide sufficient directed light to cast a shadow, but the shadow
should be such that only one side, at the edge of the object, is
sharply defined, while the other edge of the shadow, which ter-
minates on the flat surrounding surface, should gradually fade
or blur. If we have to look closely to determine that the outer
edge of the shadow is not the edge of another object, the strain
of distinguishing between the edge of an object and the edge
of a shadow makes the illumination uncomfortable and thus
unsatisfactory. In the shadows cast by a single arc in a clear
glass globe, this difficulty of distinguishing between the edge
of a shadow and the edge of an object is especially marked, and,
combined with the invisibility of objects in the shadow, makes
such shadows appear on first sight like ditches or obstructions.
In the use of shadows in illuminating engineering it thus is
necessary to have the outer edge of the shadows blur or gradually
fade, and this requires that the source of directed light be not a
point, but a sufficiently large area to scatter the light at the outer
edge of the shadow, preferably even more than is the case
with the shadows cast by the sun. This requires enclosing
the illuminant by a fairly large opal globe or other similar
device; that is, have the light issue from a fairly large luminous
area.
It must be recognized that the proper treatment of the shadows
ILLUMINATION AND ILLUMINATING ENGINEERING. 269
is one of the most important problems determining the success
or failure of an illumination.
117. Color sensitivity. The maximum of sensitivity of the
eye shifts with decreasing illumination from yellow to bluish
green, and where a low intensity of illumination is used, as in
street lighting, a source of light which is rich in the shorter
waves, that is, a white light, is superior in its physiological
illuminating value to a yellow light of the same or even
higher light flux, while inversely at high values of illumina-
tion, as for decorative purposes, the yellow light is more
effective.
Therefore it is a mistake to choose a yellow light source for
illumination of very low intensity, or a white or bluish-green
light for illumination attempting high intensity effects. Thus,
for the average street lighting of American cities, the white arc
is superior to the yellow flame arc, but, to produce a glare of light,
the latter would be superior.
While there are further physiological effects which are of im-
portance in illuminating engineering, the above four may illus-
trate the long step which exists between the distribution of the
light flux as measurable by the photometer, and the success or
failure of the illumination represented by it.
The requirements of satisfactory illumination can thus be
grouped in two main classes, referring respectively to economy
and to comfort, and the characteristics are:
(1) General or uniform, and local or concentrated illumination,
and combination of both. This is of importance for economy : to
avoid the production of unnecessary light flux; and comfort: to
reduce the effect of fatigue.
(2) Diffused and directed illumination, and combinations of
both, and the theory of the shadow. This is of importance for
the comfort of illumination, in securing clearest distinction.
(3) Quality or color of light, of importance in economy, to
suit the color to the intensity of illumination, and to comfort,
in increasing or softening differences in color shades.
(4) Massed and distributed illumination, as controlling the
distribution of the light flux, and thereby the economy and also
the diffusion.
(5) Direct illumination and indirect illumination, shaded,
diffracted, diffused, or reflected light, in its relation to the bril-
270 RADIATION, LIGHT, AND ILLUMINATION.
liancy of the light source, and thereby the effect of the contraction
of the pupil, on economy and comfort.
Some of the common mistakes made in illumination are :
(1) Unsatisfactory proportion of general and of concentrated
light.
(2) Exposure of high brilliancies in the field of vision, as naked
filaments.
(3) Unsuitable proportion of diffused and directed light.
(4) Improper direction of directed light and thereby improper
length of shadows.
(5) Sharp edges of shadows.
In order to illustrate the preceding principles, some typical
cases may be considered :
(a) Domestic lighting.
118. Domestic lighting usually requires a combination of a
concentrated illumination of fairly high intensity locally at the
work-table, dining-table, etc., and a general illumination of low
intensity, to secure comfort and economy. Occasionally, as in
halls, etc., the local lighting is absent and only general illumina-
tion required, while for instance in a sick room the general illumi-
nation is absent and only local illumination required.
In this illumination the proportion between directed and dif-
fused light should be such as to give the proper effect of shadows.
The problem of domestic illumination thus is to produce a defi-
nite distribution of light flux density, with a definite proportion
between diffused and directed light. If we deviate from the
proper proportion on one side, the room appears cold and uncom-
fortable; if we deviate in the other direction, it appears dark and
gloomy.
The light issuing directly from a single illuminant is directed
light; the light issuing from a number of illuminants is diffused
in proportion to the number of sources by the overlap of the light
fluxes of the illuminants. The light reflected from walls and
ceilings is diffused light. The proportion between the light
reflected from walls and ceilings, or the indirect light, and the
direct light from the illuminants, varies with the reflecting power
of walls and ceilings, that is, their brightness or darkness. The
proportion between directed and diffused light thus can be
changed, and the diffused light increased by increasing the num-
ber of illuminants, and also by increasing the brightness of walls
ILLUMINATION AND ILLUMINATING ENGINEERING. 271
and ceilings. With a given brightness of walls and ceilings, the
desired distribution of the light flux — a local high and general low
intensity — can be produced by a single illuminant having the
proper distribution curve of light flux. In this case, however,
usually we get too much directed, and not enough diffused, light.
The same distribution of light flux can be produced by a number
of illuminants properly located : nearer together for the local than
for the general illumination. In the latter case we get more
diffused and less directed light, and thus by choosing the number
of light sources it is possible, with any given brightness of walls
and ceilings, to get the desired distribution of light flux and at
the same time the proper proportion of directed and diffused
light. With a different brightness of walls and ceilings, the dis-
tribution curve of a single light source, required to give the
desired light flux distribution, is correspondingly changed, and,
the lighter the walls and ceilings, the more light is reflected, giving
a diffused general illumination, and thus less direct light from the
illuminant is required for the general illumination. With in-
creasing reflecting power of walls and ceilings, the proportion of
diffused light increases, and the number of light sources which
are required to give the proper proportion between directed and
diffused light is decreased, and inversely it is increased with
increasing darkness of walls and ceiling. Therefore, in a room
with light walls, a smaller number of light sources is required for
good illumination than in a room with dark walls, assuming the
same intensity of local and of general illumination.
119. The problem of domestic illumination: to get a certain
distribution of illumination, with a definite proportion between
directed and diffused light, thus leaves one independent variable
— the brightness of walls and ceilings. This is necessary, as the
problem of domestic illumination is twofold: to get the proper
illumination by means of the daylight, and also to get it for
artificial illumination. During daytime, the windows are the
source of light, the directed light issues from the windows, the
diffused light from the walls and ceilings and by the overlap of
the light from several windows. The proper distribution between
local and general illumination during daytime, and at the same
time the proportion of directed and diffused light, thus deter-
mines the number of windows and the brightness of walls and
ceilings, in the manner as discussed before.
272 RADIATION, LIGHT, AND ILLUMINATION.
As the reflecting power of walls and ceilings is fixed by day-
light considerations, it cannot be chosen, or at least only to a
limited extent, by considerations of artificial illumination, but, as
found above, this is not necessary, since by a combination of a
suitable number of light sources of proper distribution curves
the problem of artificial illumination may be solved. To some
extent, due to the quality of artificial light and daylight, the walls
can give a different reflecting power for the one than for the
other. As artificial light is deficient in blue and green, a bluish
or greenish shade of walls and ceilings gives them a greater reflect-
ing power for daylight than for artificial light — which usually
is desirable — and inversely with a reddish-yellow shade.
(b) Street Lighting.
120. The problem of street illumination is to produce a uni-
form low intensity. For reasons of economy, the intensity must
be low, at least in American cities, in which the mileage of streets,
for the same population, usually is many times greater than in
European cities, and, at the same time, the same type of illumi-
nant is usually required for the entire area of the city. The low
intensity of illumination requires the quality of light which has
the highest physiological effect at low densities, that is, white
light, and excludes the yellow light as physiologically inefficient
for low intensities. Still better would be the bluish green of
the mercury lamp, but is not much liked, due to its color. Quite
satisfactory also is the greenish yellow of the Welsbach mantel
for these low intensities. The American practice of preferring
the white light of the carbon or magnetite arc thus is correct
and in agreement with the principles of illumination, and the
yellow-flame arc can come into consideration — even if it were not
handicapped by the necessity of frequent trimming — only in
those specific cases where a high intensity of illumination is
used, as would be only in the centers of some large cities.
Uniformity of illumination is specially important in street light-
ing, where the observer moves along the street, and, due to the
low intensity, the decrease of subjective illumination by fatigue
is especially objectionable. For a street illuminant, a distribu-
tion curve is required which gives a maximum intensity some-
what below the horizontal, no light in the upper hemisphere, and
very little downward light. Street lamps therefore should be
judged and compared by the illumination given midways be-
ILLUMINATION AND ILLUMINATING ENGINEERING. 273
tween adjacent lamps, or at the point of minimum intensity, or,
in other words, by the intensity in a direction approximately
10 deg. below the horizontal. This also is in agreement with
American practice. However, it is very important that the
downward intensity be very low, and in this respect it is not
always realized that the light thrown downward is not merely a
waste of light flux, but is harmful in producing a glaring spot at
or near the lamp and, by the fatigue caused by it, reducing the
effective illumination at the minimum point between the lamps.
Most objectionable in this respect is the open direct current car-
bon arc and those types of lamps giving a downward distribution,
but even with the enclosed arc lamp the distribution of light on
the street surface is still far from uniform, and the intensity
too high near the lamp, and in this respect improvements are
desirable.
121. The greatest defects of the present street illumination,
which frequently makes it inferior in subjective illumination even
to the far lower illumination given by the full moon, are the
absence of diffused light, and especially the improper direction
and termination of the shadows, and also the high brilliancy of
the illuminant. The light of the usual street lamp is practically
all directed light, issuing in a nearly horizontal direction from a
point source. Thus the shadows are far longer than permissible,
and terminate sharply and without blur; objects in the shadows
are practically invisible, and the end of the shadow looks like the
edge of an object, thus producing a misleading effect, which
results in unsatisfactory illumination. To give a somewhat
better direction to the light requires considerable increase of the
height of the lamp above the street surface. This also would
essentially decrease the intensity of illumination below and near
the lamp, without appreciably affecting the intensity at the
minimum point, and thus would give a more uniform and thereby
better illumination. No valid reason usually exists against
greatly increasing the height of the lamps, except that of the
greater cheapness of short lamp posts, which is hardly justifiable.
It is, however, more difficult to give a proper blur to the ends of
shadows, so as to distinguish them from edges of objects. This
would require an increase of the surface of the illuminant, by
opal or frosted globe, etc. Enclosing the arc by an opal globe,
however, scatters the light more uniformly in all directions, and
274 RADIATION, LIGHT, AND ILLUMINATION.
thereby spoils the distribution curve, and interferes with the
required uniformity of illumination : with an opal globe, the
intensity in the downward direction does not differ very much
from that in the horizontal, while with lamps 20 feet above the
street level, and at distances of 200 feet from each other, the
downward intensity for uniform illumination should be not much
more than one-twenty-fifth of that under an angle of sin $ =
20
— = 0.2; or 12 deg. below the horizontal. Very much better is
-L \J{J
the effect of a frosted or sand-blasted globe. The best way of
maintaining a proper distribution curve and at the same time
diffusing the light, so as to reduce its brilliancy and blur the
shadows, appears the use of prismatic diffraction, on the principle
of the Fresnel lenses of lighthouses (holophane). Obviously,
where the lamps are close together, as in the center of large cities,
their light fluxes overlap and thereby give a better diffusion, and,
at the same time, the midway point between lamps is under a
greater angle against the horizontal ; thus a more downward dis-
tribution of the light flux permissible. For the largest part of
American street lighting, however, this does not apply.
122. In the early days of using arc lamps for American city
lighting, lighting towers were frequently used, and such tower
lighting has still survived in some cities. One or a number
of arc lamps are installed on a high tower and were supposed
from there, like artificial suns, to spread their light over an entire
city district.
This method of city lighting was found unsatisfactory, as it
did not give enough light. It is unsatisfactory, however, not
in principle, but because it was too ambitious a scheme. If,
in street illumination, we double the distance between the lamps,
each unit must have four times the light flux to get the same
minimum flux density, as the distance is doubled, and the flux
density decreases with the square of the distance. At twice
the distance between the lamps, each lamp thus must have
four times the light flux, and each mile of street thus requires
twice the power. Reducing the distance between lamps to one-
half reduces the power to one-half with the same minimum
illumination. In street lighting it is therefore of advantage to
use as many units of illuminants as possible, and bring them
together as close as possible, and correspondingly lower their
ILLUMINATION AND ILLUMINATING ENGINEERING. 275
intensity, up to the point where the increasing cost of taking
care of the larger number of units and increasing cost of poles
and connections compensates for the decreasing cost of energy.
There is a minimum which probably is fairly near our present
practice.
When, however, you come to square and exposition lighting,
you find that the distance between the illuminants has no
effect on the efficiency. Let us assume that we double the
distances between the lamps which light up a large area. Then
each lamp requires four times the light flux to get the same
minimum flux density between the lamps, but at twice the
distance between the lamps each lamp illuminates four times the
area, and the total power per square mile of lighting a large area,
like an exposition, thus is independent of the number of lamps
used, and, whether you place them close together or far apart,
you require the same total flux of light, and if you keep the same
proportions of height from the ground and distance between
lamps, you also get the same variation between maximum and
minimum intensity. But, supposing the lamps to be placed
further apart, the maximum or minimum points also are further
apart, and you get a more satisfactory illumination by having
a less rapid intensity variation. That points to the conclusion
that, for exposition lighting, the most efficient way would be to
use a relatively moderate number of high-power sources of
light on high towers at distances from each other of the same
magnitude as the height of the towers. We would get a greater
uniformity and better physiological effect by having the illumi-
nants further apart, and they would require the same total
light flux, and therefore the same power, as if you bring the lamps
close to the ground, and place them very close to each other.
The tower lighting therefore is the ideal form for lighting a large
area. When the arc was first introduced, it was so much superior
to any other illuminant known before, that people vastly over-
rated it. They thought that they could light the whole city
by it, and in trying to do so these towers would have been the
proper way, but very soon it was found that even with the effi-
ciency of the arc, to light not only the streets, but the whole
area of the city, would require an entirely impracticable amount
of light flux. It thus was too ambitious a scheme for city
lighting, but it should be done in exposition work. City illumi-
276 RADIATION, LIGHT, AND ILLUMINATION.
nation thus has come down from this first ambition to light the
whole city to an attempt to light only the streets. For the
latter purpose, however, lighting towers are inefficient, since
much of the light flux is wasted on those places which we no
longer attempt to light. In exposition lighting, however, the
most effective general illumination would be given by white
arcs on high towers, leaving the concentrated or decorative
illumination to the incandescent lamp and flame arc, of yellow
color.
LECTURE XIII.
PHYSIOLOGICAL PROBLEMS OF ILLUMINATING
ENGINEERING.
123. The design of an illumination requires the solution of
physiological as well as physical problems. Physical considera-
tions, for instance, are the distribution of light-flux intensity
throughout the illuminated space, as related to size, location
and number of light sources, while the relation, to the satisfac-
tory character of the illumination, of the direction of the light,
its subdivision and diffusion, etc., are physiological questions.
Very little, however, is known on the latter, although the entire
field of the physiological effects of the physical methods of
illumination is still largely unexplored. As result thereof,
illuminating engineering is not yet an exact science, as is, for
instance, apparatus design, but much further physiological
investigation is needed to determine the requirements and
conditions of satisfactory illumination.
The physical side of illuminating engineering: — to produce a
definite light flux density throughout the illuminated space, —
is ah engineering problem, which can be solved with any desired
degree of exactness, usually in a number of different ways.
The solution of the physical problem of light distribution,
however, does not yet complete the problem of illuminating
engineering, does not yet assure a satisfactory illumination, but
with the same distribution of light flux density throughout the
illuminated surface, the illumination may be anything between
entirely unsatisfactory and highly successful, depending on the ful-
fillment or failure to fulfill numerous physiological requirements.
Some of these are well understood and such that they can be
taken into consideration in the physical design of the illumina-
tion, and thus no excuse exists to fail in their fulfillment, though
it is frequently done. Such, for instance, is the requirement of
low intrinsic brilliancy in the field of vision, of the color of the
light, etc. Other physiological requirements are still very little
277
278 RADIATION, LIGHT, AND ILLUMINATION.
understood or entirely unknown, while on others not sufficient
quantitative data are available for exact engineering calculation.
Thus, for instance, the usual suburban street illumination,
with arcs spaced at considerable distances from each other and
located on fairly low posts, is very much inferior to the illumina-
tion given by moonlight, even when allowing for the difference
in intensity. Here the reason of the unsatisfactory character
of the former illumination is mainly the almost horizontal direc-
tion of the light flux. A perfectly vertical direction of the light
flux again is unsatisfactory in many cases, and the most satis-
factory results are given by a direction of the light flux which
makes a considerable angle with the horizontal as well as the
vertical direction. Thus, when dealing with directed light, the
direction angle is of essential physiological importance. We
have very little exact knowledge to guide in the determination
of the proper angle in which to direct the light flux ; it is known
that in general approximately horizontal and approximately
vertical direction of the light flux are objectionable, and an in-
termediary angle gives best results. However, the horizontal
direction usually is objectionable by excessive contrasts, the
vertical direction by flatness in the appearance of the illuminated
objects, and, depending on the nature of the objects, sometimes
the one, sometimes the other feature may be more objectionable.
Hence, the best angle of incidence of the light depends on the
nature, that is, the shape and location, of the illuminated objects,
on the purpose of the illumination, etc., and thus is not con-
stant, but is a function of the problem, which is still largely
unknown.
124. Not represented by the physical distribution curve of
illumination, but very marked in their physiological effect is
the difference between directed light and diffused light. In most
problems of illumination, either entirely directed light or entirely
diffused light is unsatisfactory, and a combination of directed
light and diffused light is required, as discussed in the preceding
pages. No exact knowledge, however, exists on the proportion
in which directed light and diffused light should be combined
for satisfactory illumination, nor how this proportion varies with
the nature, color, etc., of surrounding objects, with the purpose
of the illumination, etc. That it varies is well known, as for
some purposes, as a draughting room, entirely diffused light
PHYSIOLOGICAL PROBLEMS. 279
seems best suited, while for other purposes mainly directed light
seems more satisfactory.
Furthermore, the relations between directed and diffused light
have in the illuminating engineering practice been obscured to
some extent by the relation between high and low intrinsic bril-
liancy and between direct and indirect lighting. Thus, to
eliminate the objectionable feature of high intrinsic brilliancy of
the illuminant, direct lighting by light sources of high brilliancy,
which was largely directed lighting, has been replaced by indirect
lighting, by reflection from ceilings, etc., which is diffused light-
ing. Where such change has resulted in a great improvement of
the illumination, it frequently has been attributed to the change
from directed to diffused lighting, while in reality the improve-
ment may have been due to the elimination of high brilliancy
light sources from the field of vision, and engineers thereby led
to the mistaken conclusion that perfectly diffused lighting is the
preferable form. Again, in other instances such a change from
direct to indirect lighting has not resulted in the expected im-
provement, but the indirect lighting been found physiologically
unsatisfactory, and the conclusion drawn that the elimination
qf high brilliancy from the field of vision has not been beneficial,
while in reality the dissatisfaction with the indirect light was due
to the excess of diffused light and absence of directed light, and
this improper proportion between directed and diffused light
more than lost the advantage gained by eliminating the light
sources of high brilliancy from the field of vision. In this case
the proper arrangement would have been to reduce the brilliancy
of the light sources, by diffusing or diffracting globes, to a suffi-
ciently low value, but leave them in such position as to give the
necessary directed light.
Thus, in illuminating engineering, as in other sciences, it is
very easy to draw erroneous conclusions from experience by
attributing the results to a wrong cause. Any change in the
arrangement usually involves other changes: as in the above
instance, the change from high to low brilliancy commonly
causes a change from directed to diffused light; by attributing
the results to a wrong cause, serious mistakes thus may be made
in basing further work on the results.
125. In discussing diffused light, we must realize that the
meaning of " diffused light" is to some extent indefinite. To
280
RADIATION, LIGHT, AND ILLUMINATION.
define diffused light as light which traverses the space in all direc-
tions and thus casts no shadow, is not correct, since even diffused
daylight casts shadows. For instance, if in Fig. 122 P is the sur-
M/w///^^^^^
FIG. 122.
face of the ground and A a flat circular shade at distance I above
the ground, the intensity distribution of the light in plane P is as
shown in Fig. 122 for I = 0.2 A, thus showing a fairly dark
shadow beneath the center of A, but a shadow which blurs so
very gradually that with most objects it is not marked.
The light from a single point source
is perfectly directed light; it traverses
every point of space in one single
direction only, as shown as A in Fig.
123. If we now enclose the point
source in an opal globe, which then
becomes the radiator, as discussed
before, as diagrammatically shown as
B in Fig. 123, the light flux traverses
each point not in a single direction but
in all directions within a narrow angle
a, which is the angle subtended by
the radiator L from the point P.
With increasing size of the illuminant,
and thus increasing angle a, C, Fig.
123, the pencil of rays, which traverses
point P, gradually spreads, until, when
a becomes 180 deg., we get perfectly
diffused light, similar to daylight.
Hence, with a gradual change of the diameter of the illum-
inant, from a = 0 to a. = 180 deg., the light gradually changes
from directed to diffused light. Thus, no sharp dividing line
FIG. 123.
PHYSIOLOGICAL PROBLEMS. 281
can be drawn between directed light, and diffused light, but
the directed light from a light source of considerable diameter
(that is, a diameter which is not neglible compared with the dis-
tance of the illuminated objects from the light) already has to
some extent the character of diffused light.
Diffused light thus may be denned as light given by a radiator
which subtends a spherical angle equal to a considerable part of
the sphere. This makes the term "diffused light" a relative
term. Near to a radiator of considerable size, the light given
by this radiator thus is largely diffused light, while at considerable
distance it is practically directed light, or, in other words, the
light given by light sources of considerable size is directed light
only at such distances from the radiator at which the law of
inverse squares holds; but approaching the radiator so far
that this law of inverse squares (flux density inverse proportional
to the square of the distance) does not hold, the light approaches
somewhat the character of diffused light.
The physiological effects, however, during a gradual change
from a = 0, or directed light, to a = 180 deg. , or diffused light,
apparently do not change uniformly, but new effects appear
and others disappear.
126. The main objection to directed light from a single source
results from the absence of light in the shadows. Using, how-
ever, two or more illuminants, that is, combining directed light
of several widely different directions, the shadow cast by one
illuminant is illuminated by the other illuminants, and thus an
effect produced very similar to diffusion. Thus with two light
sources, at a point at which both light sources give the same
illumination, the intensity in the shadow cast by one illuminant
is still 50 per cent, that is, the illumination the same as if equal
volumes of directed and of diffused light were combined, and
to a considerable extent the physiological effect is the same.
It is not completely so, however. In the illumination by equal
volumes of diffused light and directed light from a single source,
each object casts a single shadow, in which the illumination is
reduced to half. When producing an equivalent diffusion by
two light sources, an object casts two shadows, in which the
illumination is reduced to half (if the two light sources give
equal illumination), but, where the shadows overlap, a perfectly
black and lightless shadow is produced. The more the two
282 RADIATION, LIGHT, AND ILLUMINATION.
half shadows overlap to a complete shadow, the less the combina-
tion of the two light sources is equivalent to diffusion. At
the same time, occasionally the existence of two or more half
shadows and of their compound shadows may assist distinction,
and thereby be advantageous. In short, there is a vast and
largely unexplored field in the physiology of illumination,
which the illuminating engineer will have to study and investi-
gate.
While one point source of light gives directed light, two
sources at distances from each other give an effect equivalent
to diffusion, and three or more sources still more so, until in the
theoretical case of an infinite number of point sources distributed
through space — or, practically, a very large number of distrib-
buted illuminants — we get perfect diffusion. With a change
from a single to a very large number of illuminants, the illumi-
nation thus changes from directed to diffused, and thus, for
a moderate number of illuminants, is intermediate between
directed and diffused, but nevertheless this intermediate state is
physiologically of entirely different character from that given
by a single illuminant of very large diameter, that is large
angle a, as discussed above.
127. We thus have true diffused light, as daylight, the equiva-
lent diffusion given by the combination of several light sources,
which depends on their relative location, and the equivalent
diffusion given by a large relative diameter of the light source.
The latter again varies with the shape of the light source, and
in extreme cases, as a linear straight radiator, as a Geissler tube
(Moore tube), we may get an illumination which, at any point
of space, is practically diffused in one direction, and practically
directed in a direction at right angle to the former. In such
cases we again get different physiological phenomena. For
instance, a straight rod, held parallel to the radiator, casts a
sharp black shadow — directed light — while, when held at right
angles to the radiator, it casts no shadow — diffused light. With
objects of more irregular shape, it can be seen that the shape
and appearance of the shadows give a rather interesting problem,
and the physiological impression made by such illumination
thus is different again, from that of ordinary directed or diffused
light or their combination.
In general, wherever two or more illuminants are used, the
PHYSIOLOGICAL PROBLEMS. 283
physiological effect depends on the relative position of the light
sources to the illuminated objects, irrespective of the intensity of
illumination. Thus, for instance, in the illumination shown in
Fig. 117, on the same curve of equal illumination, the physiologi-
cal effect is not constant, but varies from point to point. On the
curve of 850 near the center of the room, an object casts four
shadows of approximately equal intensity, in different direc-
tions. The shadows are sufficiently marked to assist in seeing,
and the illumination in the shadow is quite high ; thus the illumi-
nation is very satisfactory. On the same curve 850, near the
edge of the room, the four shadows fall in nearly the same
direction, only one is marked, and by the overlap of the shadows
a large compound shadow is formed, in which the illumination
is very low, distinction difficult, and the illumination thus
unsatisfactory. Thus with the same physical value of illumina-
tion, on the same curve 850, the physiological effect in this case
changes from a very satisfactory illumination at one place,
to a quite unsatisfactory illumination at another place. Thus,
in this instance, while the solution of the illuminating problem,
given in Fig. 117, is physically perfect, that is, the illumination
very uniform throughout the entire room, and the efficiency
high, physiologically the illumination is satisfactory only in
the middle of the room, but becomes more and more unsatisfac-
tory the further we go outside of the square formed by the four
light sources. Physiologically the illumination would probably
be improved by locating the light sources in the four corners
of the ceiling, or in the centers of the four sides of the ceiling.
Physically, this arrangement of lamps in the corners of the room
would greatly reduce the efficiency, thus require either more
power, or lower the average illumination; the arrangement of
the lamps at the sides would decrease the efficiency less, but
would considerably impair the uniformity of illumination, giving
a lower illumination near the corners of the room.
Furthermore, in illuminating engineering, enters as an impor-
tant and largely unknown factor, the effect on the physical and
physiological illumination, of the objects in the illuminated
space, and of the observer] that is, the light flux distribution
and its physiological effect, as depending on the location of
light sources and distribution of their light flux through the
illuminated space, is not sufficient to solve the problem of
284 RADIATION, LIGHT, AND ILLUMINATION.
illumination, but consideration must be given to the changes
resulting from the use of the illumination. For instance, in
the illumination shown in Fig. 117, and discussed above, the
diffused light, 0.250, resulting from reflection from walls and
ceiling, is quite considerable, and would be nearly sufficient
for giving distinction in the compound shadow of all four illumi-
nants, as it exists in a pronounced degree near the walls. Thus
even there the illumination would be moderately fair. How-
ever, when relying on this diffused illumination to see in the
shadow of objects close to the walls, it may not be present, or
largely reduced by the shadow of the observer, since, as seen
above, diffused light also casts shadows, though the blur at
the edges of these shadows is such as to make them very little
noticeable. Thus, when approaching close to the walls to look
at an object, we may find it shaded from the direct light and
from most of the diffused light, thus giving unsatisfactory
illumination. Locating the light sources in the corners or the
centers of the sides of the room, we get pronounced shadows
of the objects located against the walls of the room, and thereby
again unsatisfactory illumination, although in this case, physio-
logically, considering merely the room without the objects which
may be located in it, the illumination would be satisfactory.
Thus we may have to sacrifice uniformity of illumination still
further, by arranging five light sources, four in the corners
of centers of the sides of the room, and one, of larger light flux,
in the center of the ceiling.
Thus, occasionally, illuminations designed for uniform flux
density are not satisfactory, even though the proportion of
directed and of diffused light, and the direction of the directed
light, is physiologically correct, because the changes resulting
from the objects in the room, and the person of the user of the
illumination, are not sufficiently considered.
129. The cause of most of these difficulties in dealing with
illuminating problems is that, physiologically, light is not a
vector quantity; that is, light flux densities cannot be combined
by the parallelogram law.
Two magnetomotive forces A and B, Fig. 124, acting on the
same point P, combine by the parallelogram law to a resultant
C; that is, the combined action of A and B is identical with the
action of a single m.m.f. C. Thus the m.m.f. existing at any
PHYSIOLOGICAL PROBLEMS.
285
point P of space is perfectly characterized by two quantities
only — the resultant intensity, C, and its direction.
If, however, in Fig. 125, A and B represent the two light
flux densities produced at point P by two light sources I/t
and L2, their physiological and also their physical action may
be entirely different from that of one light flux C derived by
combining A and B by the parallelogram law.
FIG. 124.
FIG. 125.
In some respects the action of the two separate flux densities
A and B is the same, or nearly the same, as that of a resultant
flux density C; the illumination of an opaque plane a, located
so that both light sources Ll and L2 are on the same side of the
plane, is the same. If, however, the illuminated plane is trans-
parent or translucent, and also in regard to the effects of polariza-
tion, reflection etc., the effect of the two separate flux densities
A and B differs from that of a single resultant C. Entirely
different is the effect if the light sources Lt and L2 are on dif-
ferent sides of the plane. Thus, with a plane c located in the
direction C, the resultant flux density C would give no illumina-
tion, while in reality by A and B both sides of the plane are
fairly well illuminated. Thus, with the plane in any direction
within the angle cu between PL2 and PA, it receives the same
amount of light from A and B as it would receive from (7; but
in any direction within the angle T = 7t — to, between PA and
PB, it receives more light from A and B than it would receive
286
RADIATION, LIGHT, AND ILLUMINATION.
from the resultant C, and receives infinitely more light in the
direction c (that is, in this direction it receives no light from C).
Within this angle T, both sides of the plane are illuminated
by A and B, which obviously is never possible by a resultant
vector C.
In the illumination of a plane, the differences between the ac-
tual illumination by A and B and the illumination which would
result, if light were a vector quantity, by (7, are only those of
intensity of illumination. With an object of different shape,
however, the phenomenon becomes far more complex. Thus the
illumination of a sphere S by the resultant C would be as shown
in Fig. 126, — half the sphere dark, the other half light, and with
a maximum intensity at c, shading off towards zero at the termi-
nator mn. The actual illumination as shown in Fig. 127 gives a
FIG. 126.
FIG. 127.
black segment of angle <D, while more than half the circumference
of the sphere is illuminated. The maximum intensity is at the
same place c, and of the same intensity as in Fig. 123 but
the total light flux received by the sphere is far greater than
would be received from the resultant C, and is the sum of the
light fluxes received from the two light sources. Thus :
In the illumination of a sphere the light flux densities are
added, irrespective of their direction, and not vectorially com-
bined.
In the illumination of a plane, by light sources which all lie
on the same side of the plane, the light flux densities are vectori-
ally combined.
PHYSIOLOGICAL PROBLEMS, 287
With other shapes of objects, the total received light flux may
even be more than corresponds to the sum of the component flux
densities.
As in general illumination for distinguishing objects we have
to deal with all possible shapes, it thus follows that for the gen-
eral problem of illumination the resultant effect is most nearly
related to the "total flux density" or "total illumination" as
derived by adding, irrespective of their direction, all the light
flux densities, as was done in the preceding lectures when dealing
with light flux distribution. Only in special cases, as the illumi-
nation of a draughting table, the flux density in one particular
direction is of importance, and was used as the " horizontal illu-
mination" in the instance represented by Figs. 119 to 121.
130. While the resultant effect, or the total illumination, is de-
rived by adding the flux densities irrespective of their direction,
in the physiological effect, that is, the appearance, the direction
plays an essential part. Thus a sphere located as in Fig. 127
looks different than it looks in Fig. 126, even if it receives the
same total light flux. Still more marked is this difference with
more complex shapes of the illuminated objects. Thus a land-
scape looks different with every different position of the sun in
the sky, and different again in the diffused light of a cloudy day,
irrespective of the intensity of the illumination. Under some
conditions sharp contrasts appear, where under other illumina-
tions the appearance is flat, and with the change of illumination
contrasts disappear in some places, appear in others, etc.; that
is, the appearance of a complex body very greatly varies with
the character of the illumination, entirely independent of its
intensity.
With artificial illumination it then is the problem of the
illuminating engineer to design the illumination so as to bring
out contrasts where required by the purpose of the illumination,
reduce them where too great or unnecessary, etc. If we consider
the possible personal equations of the user of the illumination
as depending on his physical nature, occupation or state, further-
more the effect of the color of light and the marked physiological
effect which even slight variations in the color shade produce, it
can be seen that the success of illuminating engineering prob-
lems still largely depends on the judgment of the designer, and
this judgment is not yet guided by any extended exact experi-
288 RADIATION, LIGHT, AND ILLUMINATION.
ence, thus rather uncertain. An enormous amount of work is
still to be done mainly in the field of "engineering physiology/7
before the design of a system of illumination can approach the
same exactness as for instance the design of long-distance trans-
mission or other engineering work.
INDEX.
PAGE
Absolute color in illumination 265
Absorption of excess of light flux 261
of light by body 28
spectrum 27
Acclimatization to radiation 59
Acetylene flame 130
standard 178
Acoustic scale of frequency 14
Actual or objective color 33
Adaptability range of eye 38
Albedo of ceiling 246
radiator 85
reflector 212, 215
walls 246
whiteness 30
Allotropic modifications of carbon 81
Alternating arc 114, 116, 125
Alternating current field, frequency and wave length 17
as polarized wave 8
Amyl acetate lamp 177
Analytic action of animal organism 65
Angle of directed light 278
Angstrom unit 7
Animal organism, analytic action 65
Apparent or subjective color 34
Arc characteristics 138
conduction 105
conductor 105, 110
electric 98
efficiency of light production 122
flame 110
Arcing ground, frequency and wave length 17
Arc lamps 151
photometry 182
rectifier 114
spectrum 105
stability curve 144
stream 105
street illumination 234
as unidirectional conductor 113
289
290 INDEX.
PAGE
Arc voltage curve 139
Area lighting 275
Armature reaction of arc machine 163
Artificial illumination, domestic lighting 271
more harmful than daylight 54
Auxiliary arc starting main arc 112
Band spectrum 26
Base filament 81
Beam of searchlight, intensity 234
Biological phosphorescence 96
Black 32
body 29
radiation 84, 88
of hydrocarbon flame , 134
Blood, opaque for ultra-violet light 58
transparent for long light waves 58
Blue light, specific effect 51
Blurring of the shadow in illumination 268
vision 54
Borides as refractory bodies , 78
Bolometer measuring radiation power 166
Brightness of walls and ceiling in domestic lighting 270
Brilliancy and contraction of pupil 262
of light sources 256, 259
objectionable effect 263
of radiator 189, 221
Brush arc machine 163
Brush discharge 101
Bunsen photometer 170
Burns by radiation 48
Calcium arc, orange yellow 123
carbide arc 124
Calculation of room illumination 247
street illumination 238
Candle 128
power 186
equivalent 258
standard of light 177
unit of light intensity 257
Carbides as refractory bodies 78
Carbon, allotropic modifications 81
arc 140
distribution 203
efficiency 122
electrode as radiator 190, 193
INDEX. 291
PAGE
Carbon, arc, incomplete rectification 117
lamp as incandescent radiator 76
not a typical arc 109
in street illumination 236, 240
bisulphide lamp 135
filament as radiator 195
as refractory element 77
vapor tension 79
Cathode of arc 108
Ceiling, albedo 246
Change carbons 82
Characteristics of the arc 137
Chemical action of light 63
on plants 64
luminescence 97
of flame 133
phosphorescence 95
rays 63
Chimney of luminous arc lamp 158
Chlorophyl 64
Circular cylinder as radiator 197
line as radiator 197
plane as radiator 190
shading circular radiator 203
shading linear radiator 210
radiator shaded by circular plane 203
Circulating flame lamp 126
Clutch of arc lamp 153
Cold light 48
Color change of light of arc 118
differences in illumination 265
photometry 172
Colored 33
body 29, 31, 36
lights, comparison 42
radiation 85
radiator of magnesium flame 134
Color effect in illuminating engineering 269
street lighting 272
Colorless 32
body 29, 31, 36
Color of light and economy 269
fatigue 265
Combination of light fluxes by addition 285
Comfort and economy in domestic lighting 270
Comparison of arcs for street lighting 236
colored light 42
292 INDEX.
PAGE
Comparison of globes regarding light flux distribution 224
illumination curves 232
radiators 202
and shadows 209
reflectors 215
Concentrated illumination 260
or local illumination 269
Conduction, continuous 98, 105
disruptive 98
Constant current system of arc lighting 162
Constructive action of plant 65
Continuous conduction 98, 105
spectrum 26
Continuity of the arc at the cathode Ill
Contraction of pupil 38, 262
Control of subjective color in illumination 265
Core of arc flame 110
Corona 101
Crater of the arc as radiator 191
Crookes' radiometer 10
Cylindrical radiator 195
Daylight illumination, domestic lighting 271
Defects of street lighting 273
Density of light flux , 256, 259
Destructive effect of radiation 48, 57, 59
short ultra-violet light 52
Dielectric constant and refractive index 24
Differences of color in illumination 265
intensity in illumination 265
Differential arc lamp 156
Diffracting globe and light flux distribution 223
Diffraction grating 26
and light distribution 221
spectroscope 26
Diffused and directed light 267, 269
illumination 251, 266
in indoor lighting 246
light, definition 279
and directed light, proportions 278
shadow 280
Diffusing globe and light flux distribution 223
Diffusion, equivalent 281
and light distribution 221
by number of radiators 281
by size of radiator 280
Directed and diffused light 267, 269
INDEX. 293
PAGE
Directed light 266
angle of direction. . . .• 278
Direct and indirect illumination 269
Discontinuity of the arc at the anode 112
Disease germs, action of light 61
Disinfecting action of light 60
Disruptive conduction 98
voltage 99
and gas pressure 100
Distinction between arc and Geissler discharge 106
of objects by shadow .' 267
Distributed and massed illumination 269
Distribution curve and design of incandescent lamp 243
of frosted globe 221
of light 180, 187, 256
of opal globe v 221
in street lighting 272
Domestic lighting 226, 270
Double refraction 9
Downward candle power 184
Ear as analytic organ 21
Economies of flame arc lamp 212
Efficiency and arc length 146
of illuminant 186
light production by arc 118, 122
light production by incandescence 74, 81
room illumination 253
Electric waves, engineering importance 18
frequency 15
Electro-conduction feeding arc 123
Electro-luminescence, efficiency 126
of gases and vapors 98
solids 95
Ellipse, circumference 198
Emulsions as translucent bodies 32
Enclosed arc efficiency 148
carbon arc 160
in street lighting 236
Energy of plant life derived from radiation 65
Engineering physiology 288
Equatorial distribution of light 181
Equiluminous curves 251
Equivalent candle power 258
diffusion 281
Etched glass globe, diffraction 221
Ether. . 7
294 INDEX.
Ether as carrier of energy 7
form of matter 7
Euler's theory of radiation 4
Evaporation of carbon 79
Exposition lighting 275
Eye perceiving only the resultant 21
structure of 37
Fatigue and color of light 265
of the eye 263
optic nerve 38
Fechner's law 39
Feeding device of arc lamp 151
Filament, single loop, distribution curve 199
Fire-fly, light of 96
Fireworks 98
Fixed arc length of luminous arc 158
Flame arc distribution 212
Flame carbon arc 123, 160
distribution 212
Flames as illuminants 128
Flicker photometer. 173
Flickering of the arc 110
Floating system of arc control 156
Fluorescence 66, 94
spectrum ! 27, 69
Fluorescent bodies 30
Flux of light -256, 259
Frequency converter of radiation 13, 31
of radiation 7
and temperature 73
scale of acoustic 14
of ultra-violet radiation 14
Frosted globe 262
diffraction 221
Gas flame 128
pressure and disruptive voltage 100
Gasolene deposited carbon 81
flame 128
Geissler discharge 98
tube efficiency 104
glow 100
lighting 104
General illumination 260
or uniform illumination 269
German candle 178
INDEX. 295
PAGE
Germicidal action of light 60
Glass, opaque for ultra-violet light 13
as protection against ultra-violet light 55
Globes, comparison of light distribution 224
Glow of Geissler tube 100
Grey body 30
radiation 84, 93
Gypsum, transparent for ultra-violet light 13
Harmful effect of light on vegetation 56
radiation 48
violet and ultra-violet 52
Harmless radiation 48
Harmlessness of artificial illuminants 56
Harmonics of radiation 20
Heat evaporation feeding arc 123
Heat evaporation from positive terminal of arc 109
luminescence 91, 93, 96
at positive terminal of arc 109
radiation 1
rays 63
Hefner lamp 178
Helium 78
Hemispherical candle power 185
Hertzian waves, frequency and wave length 16, 17
High frequency currents, frequency and wave length 17
light, therapeutic action 61
Hollow circular surface as radiator 191
Holophane globe 262
Horizontal candle power of incandescent lamp 258
illumination 226, 287
of room 253
intensity 184
of light 182
table illumination 253
Hydrocarbon flames 128
Hydro-oxygen flame 136
Iceland spar 9
Illuminant 256
Illuminating engineering 256
Illumination 177, 179, 256, 259
Illumination curves 226, 229
of arcs for street lighting 236
comparison 232
of incandescent lamp 244
of table by incandescent lamps 254
296 INDEX.
PAGE
Illumination, horizontal 226
objective 261
problems 260
of streets by arcs 234
subjective 262
of table by incandescent lamp 253
total 226
uniform 226
vertical 227
Illuminometer in indoor illumination 253
Imperfectly transparent bodies 31
Incandescent lamp 76
design and distribution curve 243
illumination 242
photometry 182
Indirect and direct illumination 269
lighting 262
Indoor illumination, calculation 247
by incandescent lamps 242
Inflammation of the eye by ultra-violet light 53
radiation 48
Infra-red rays 12
Integrating photometry 183
sphere and photometry 184
Intensity curves of arcs for street lighting 256
comparison 232
comparison of radiators 197
differences in illumination 265
of light 257
of light source 256, 259
Interference , 6
rings 6
Intermediary color in photometry 172
Intermediate carbon 83
International candle 178
Intrinsic brilliancy, see Brilliancy.
Iridescence 6
Iron arc 119
giving ultra-violet light 13
Irregular reflection 28
and light distribution 212
Irritation by uniform intensity of illumination 264
Kerosene lamp 128
Kirchhoff's law of radiation 85
Lamps, arc 151
Light flux . . 177, 186, 256, 259
INDEX. 297
PAGE
Light flux, combination by addition 285
comparison of radiators 197
density 177, 256, 259
distribution by frosted globe 223
distribution by opal globe 223
as germicide 60
intensity 177, 186
measurement 166
Lightning phenomena frequency and wave length 17
Light not a vector quantity 284
as physiological effect 168
production by incandescence 74
also see Radiation.
sources, comparison 202, 209, 215
and enclosing globe, comparison 224
intensity 256, 259
as transversal vibration 8
Lighting, tower 274
Light unit 177
as wave motion 6
Lime light 136
Limits of electrical waves, frequency and wave length 17
frequency of electric waves 16
Linear radiator shaded by circular flame 210
Line spectrum 26
of arc 118
Local or concentrated illumination 269
illumination 226, 260
and uniform illumination 264
Logarithmic scale of frequency 14
law of sensation 38
Long burning carbon arc 160
Longitudinal vibration 7
Lumen 186
as unit of light flux 257
Luminescence 94
of arc 117
chemical 97
of flame 133
by heat 91
Luminometer 43, 174
chart 175
Luminous arc 123, 160
distribution 210, 215, 220
efficiency 149
lamp 157
radiator 195
298 INDEX.
PAGK
Luminous arc in street illumination 240
flame 129
Magnesium flame 134
Magnetite arc 123
constants 140
distribution 220
in street lighting 236, 240
Magnetite arc as typical arc 109
Massed and distributed illumination 269
Maximum candle power 184
visibility 46
Mean spherical intensity 180, 184, 257
Measurement of light and radiation 166
Mechanical equivalent of light 42
Mechanism of arc lamp . 152
Melting points of elements 77
Mercury arc, constants 140, 145
greenish blue 123
higher frequency of ultra-violet light 13
rectification 117
rectifier 114
rectifier system 165
tube as radiator 195
Meridian curve of light 180, 188
Metal arcs and ultra-violet light 56
unsteadiness 125
Metallic carbon 81
Metals as most opaque bodies 31
Methane 128
Mica opaque for ultra-violet light 13
Micron 7
Micro-organisms, effect of light 61
Milk glass globe diffusion 221
Minimum visible amount of light 45
Mirror 28
reflector and light distribution 215
Misleading character of meridian curves of light 188
polar curves of light 187
Modifications of carbons 81
Negative carbon electrode shadow 203
spot of arc 107, 110, 125
terminal, also see Cathode.
determining character of arc 108
Newton's theory of radiation 4
Normal temperature radiation 75, 84
INDEX. 299
PAGE
Objects, effect on light distribution 283
Objective or actual color 33
color in illumination 265
illumination 261
Observer, effect on light distribution 283
Octave as frequency scale 14
Oil lamp 128
Opal globe 262
diffusion 22 1
and nature of shadow 268
Opaque 32
body 31
colors 32, 36
Open arcs, efficiency 148
Open carbon arc 160
Oscillations, electrical, frequency and wave length 17
Osmium lamp 79
Overlap of light fluxes in illumination 267
Oxygen in flame 132
Ozone production by ultra-violet light 64
Paraffine candle 131
photometer 171
Parallelogram law and light flux 284
Pathogenic bacilli, effect of light 61
Pathological effects of radiation 57
Pentane lamp 178
Periodic system of elements and radiation efficiency 77
Permeability and refractive index 24
Personal equation of user in illuminating engineering 287
Physical phosphorescence 95
Physiological effect of sensation 40
in light measurement 167
measure of light 168, 186
problems of illumination 262
illuminating engineering 277
unit of light 177
Phosphorescence 66, 94
Photography 63
Photometry 169
Phototheraphy 61
Pigment in acclimatization 59
Plane illumination 286
as radiator 190
Plants, action of light 64
Point as radiator 189
Polar curves of light distribution 187
300 INDEX.
PAGE
Polarized wave 8
Positive terminal of arc 109
also see Anode.
Power burn 53
effect of radiation 57
Primary standard color 179
standards of light 177
Prismatic reflection and refraction 221, 224
Problems of illumination 260
Protection against ultra-violet light 55
Protective device of arc lamp 151
mechanism of the eye against radiation 50
Protoplasm, effect of radiation 57
Pulsations of arc voltage 159
Pupil contraction 262
Putrefactive bacilli, effect of light 60
Pyro-luminescence 96
Pyrometers, visual 90
Quality or color of light 269
Quartz as most transparent body 31
transparent for ultra-violet light 13
Radiant heat 1
Radiation efficiency 86
as a form of energy 1
measurement 166
measured as power 166
power 72
also see Light.
Radiators, comparison 202, 209
of light 187
separate from flame 135
Radio-active substances 14
Radio-fluorescence 95
Radio-luminescence 95
Radio-phosphorescence 95
Radio-therapy 61
Radium rays, harmful effects of 58
Range of frequencies of radiation 17
Reading distances measuring light 174
Rectification by arcs 114
Rectifying range of arc voltage 116
Red fluorescence 67
light, chemical action of 64
therapeutic effect 62
lines of mercury arc spectrum 120
INDEX. 301
PAGE
Red mercury arc 121
Reduction factor of incandescent lamp 182
Reflected light from walls and ceiling, calculation 250
Reflection affecting light distribution 212
of light by body 28
regular, and light distribution 215
and shadow with radiator 219
Reflectors, comparison 215
as secondary radiators 212
as virtual radiators 215
Refraction law 23
and light distribution 221
spectroscope 25
Refractive index 23
and dielectric constant 24
and permeability 24
Regenerative flame lamp 126
Regular reflection 28, 215
and refraction 224
Regulator of arc machine 164
Reversed spectrum 27
Ring carbon 82
Room illumination, calculation 247
by incandescent lamp 242
Rounded circular surface as radiator 193
Sand blasted globe, diffraction 221
Saprophytic bacilli, effect of light 60
Searchlight beam, intensity 234
Secondary radiator and reflector 212, 216
Selective radiation 87
Sensitivity curve of the eye 43, 47
Sensitivity of the eye 263
and frequency 40
to ultra-violet light 54
maximum, of the eye 46
Separate radiator of flame 135
Series arc lamp 157
system of arc lighting 162
Shadow 202
blurring of, in illumination 268
of diffused light 280
in illuminating engineering 266
of negative carbon 203
of negative terminal of arc 148
number of 268
proper intensity in illumination 266
302 INDEX.
PAGE
Shadow photometer 171
in street lighting, defective 273
theory of 269
Shell of arc flame 110
Short burning carbon arc 160
Short ultra-violet light, destructive effect 52
Spherical intensity 257
Signal lights, color 98
Silicides as refractory bodies 78
Single loop filament, distribution curve 199
Smokiness of flame 130
Smoky flame 129
Sound as longitudinal vibration 8
waves, frequency and wave length 17
Spark voltage 100
Specific effects of high frequency radiation 51
Spectrum of arc 118
and negative terminal 108
by diffraction 26
of flames , . 134
of luminescence 96
of radiation 17
by refraction 25
Sphere, illumination 287
as radiator 189
Spherical intensity 180
reduction factor of incandescent lamp 182
Stability curve of the arc 142, 144
limit of arc 143
Stable branch of arc characteristic 142
Standard candle 170
Starting of arc 106
by auxiliary arc 112
device of arc lamp 151
Steadying device of arc lamp 151
reactance or resistance of arc lamp 151
Stephan's law 70, 75
Stimulating effect of radiation 57, 59
Straight line as radiator 195
Street illmination by arcs 234
comparison of arc lamps 240
Street lighting 226, 272
calculation 238
comparison of illuminants 236
defects 273
Striated Geissler discharge 101
Subjective or apparent color 34
INDEX. 303
PAGE
Subjective color, control in illumination 265
illumination 262
Sulphur flame 135
Sunburn 59
Sun spectrum 27
Surges, electrical, frequency and wave length 17
Symptoms of ultra-violet burns 54
Synthetic action of plants 65
Table illumination 253
Tanning 59
Tantalum lamp 80
Temperature of arc stream 108
of carbon filament 79
and frequency of radiation 73
of maximum efficiency of light production 74
measurement by radiation law 89
radiation 70
of flame 128
law of 84
standard 178
Therapeutic use of light 61
effects of radiation 57
Thermo-couple measuring radiation power 166
Thermo-luminescence 95
Threshold value of visibility 45
Titanides as refractory bodies 78
Titanium arc, white 123
carbide arcs 117, 123
Total illumination 226, 287
of room 253
Tower lighting 274
Transfer of arc between anodes 112
Transient electric phenomena 18
Translucent body 31
Transmission of light by body 28
Transparent 32
body 31
color 31, 32, 36
Transversal vibration 7
Tungsten lamp 80
as refractory element 78
Also see Wolfram.
Typical arc 109
Ultra-red rays 12
frequency and wave length 14, 17
304 INDEX.
PAGE
Ultra-violet arc lamp 12
burn 53
burn in wireless telegraphy 54
iron arc 119
lamp 135
light of arc 55
light and fluorescence 67
light harmful effect 62
therapeutic action 61
radiation, frequency 14
rays 12
frequency and wave length 17
Unidirectional conduction of electric arc 113
Uniform distribution illumination curve 229
or general illumination 269
illumination 226, 260
in street lighting 235
Uniformity in street lighting 272
Uniform and local illumination 264
total illumination 228
Unit of light 177
Unstable branch of arc characteristic 142
Unsteadiness of jaetal arcs 125
Vacuum arc 145
Vapor pressure of the arc 105
stream of the arc 105
tension of carbon 79
Vector quantities and light 284
Velocity of electrical radiation 4
light 2
in a medium 23
Vertical illumination 227
Violet light, harmful effect 52
specific effect 52
Violle standard of light 177
Virtual radiator 221
and reflector 216
Visible light, frequency and wave length 17
radiation 10
power measurement 168
range . „ 14
and temperature 74
Visibility range of radiation 37
Visual pyrometers 90
Walls, albedo 246
Warm light 48
INDEX. 305
PAGE
Waste of light flux by absorption 261
Water as transparent body 31
Wave length determination 6
of visible radiation 10
Welsbach mantle 92, 136
White 32
body 29
iron arc 1 19
Whiteness or albedo 30
Willemite fluorescence 13
Wireless telegraph waves, frequency and wave length 15, 17
ultra-violet burn 54
Wolfram as refractory element 77
also see Tungsten.
X-ray frequency and wave length 14, 17
harmful effects of 58
specific action 56
Zinc arc, constants 140
rectification. . 117
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